Simon Hopkinson first met Elizabeth David in 1984, or thereabouts, at Hilaire, the Chelsea restaurant of which he was chef. She came for supper with Valerie Eliot, and the widow of the poet was wearing – he remembers it vividly – a polka-dot dress. "I was very excited," he says. "Because I was a fan." By this time, David was in her early 70s and a little frail (in the early 1960s, she had suffered a cerebral haemorrhage, and in the 1970s, she was in a serious car accident). As a result, she had a miniature appetite. "She ate like a bird. But I remember that I'd made a consomme, very clear and gorgeous, from some prawn shells. She asked for a second helping, and I was so pleased." Made brave by this, at the end of her lunch, the young Hopkinson left his kitchen, clutching a copy of An Omelette and a Glass of Wine, David's collected journalism and the book of hers that he loves the most. She duly signed it for him, and so began a friendship that would last until she died in 1992.

At first, their relationship consisted mostly of conversations snatched when she came to lunch at Hopkinson's next berth, Bibendum, of which she was very fond (she sometimes came with another pal, the food writer Richard Olney). In time, though, the two of them became closer, and Hopkinson would take her out, or visit her at home in Halsey Street, Chelsea. On one occasion, they went to the River Café: its chef-proprietors, Ruth Rogers and Rose Gray, having been warned, were wearing T-shirts with David's recipe for chocolate – or was it almond? – tart printed on the back (she took this in good part). On another, they celebrated her birthday at home with Jill Norman, David's long-time editor, and a bottle of Dom Pérignon, nibbling all the while on her favourite Roka cheese biscuits. Hopkinson was even able to introduce her to one of his most famous regular customers, Francis Bacon. The artist was – this seems so wonderfully unlikely – another fan of David's, and kept her books, as so many people do, beside his bed. "That was exciting," says Hopkinson. "Two completely different geniuses shaking hands." Oh, that he had pulled out a camera and taken a photograph.

David could be difficult; this is no secret. But Hopkinson knew how to handle her. "Well, I knew never to bring up the Carrier word," he says [a reference to Robert Carrier, the American cook and television presenter whose recipes were almost as rich as his to-camera style]. "And if you didn't agree with her, those little, beady eyes would pop right open. She could be … vociferous. One was on one's mettle, put it like that. She could be pedantic, too. My thing about crisp and crispy [he loathes the latter word] came from her in the beginning. She pointed it out one day, the fact that the extra 'y' is completely unnecessary, and I thought: yes, you're right. But I had huge respect for her. She was so learned and intelligent, and I loved the way she looked. Those eyes. She was so delicate. I remember seeing her tucked up in bed, recuperating, Post-it notes everywhere – all the things she wanted to moan about – and the room full of beautiful things."

Somewhere in his flat is an ancient answer phone, on which there remains the last message she left him. David died in the early hours of 22 May 1992, having enjoyed a good bottle of chablis and some caviar brought to her bedside by friends. A memorial service was held at St Martin-in-the-Fields on 10 September, after which a lunch was held at the Institute of Contemporary Arts in the Mall, the food provided by the chefs Sally Clarke, Martin Lam and, of course, Hopkinson. What did he make? "Piedmontese peppers, and spiced aubergine salad, a particular favourite of hers." The recipe for the latter – fragrant with cumin, allspice and fresh coriander – can be found in his book Roast Chicken and Other Stories. It is completely delicious and, if you follow the quantities exactly, somehow magically abundant.

What does Hopkinson make of David's legacy now, in the month of the centenary of her birth on Boxing Day 1913? He can only speak personally. "The writing had a big impact on me; you have to really want to cook to use her, it's not just a case of following a recipe. You have to pay attention. I loved the short ramble around, and then the perfect recipe within. But someone once told me Jamie Oliver had sold more copies of just one of his books than have been sold of Elizabeth's entire oeuvre, and what can you say about that?" He sighs, theatrically. As to her wider influence, the powerful effect she famously had (or not) on British palates, he believes this was as much a question of timing as anything else. David, whose first book, A Book of Mediterranean Food, was published in 1950, arrived on the scene at just the right moment: the British middle classes, exhausted by austerity, were longing, even if they did not precisely know it, for the taste of sunshine. David was, moreover, able to forge her career in an environment more suited to her particular talents and personality: "She wouldn't have been able to do television, and she wouldn't have wanted to do it either." The life of the celebrity was not for the redoubtable Mrs David. Hopkinson could no more have imagined her posing for the cover of a glossy magazine, dripping spatula in hand, than he could dashing to the nearest McDonald's for a Big Mac and fries.

To understand Elizabeth David, and her place in the history of the mysterious eating habits of these islands, one must have some sense of what it was like to live through the second world war. Last summer, I spent several days in the British Library reading austerity cookbooks: survival manuals for housewives who had to cope with the rationing that would outlast the war by several years (butter, cheese, margarine, cooking fats and meat did not come off the ration until 1954). In my locker downstairs, my (Elizabeth David-approved) lunchtime sandwich of prosciutto and brie patiently awaited my return, but even so, it was a dispiriting business. Before me were the least appealing recipes ever written: mock marzipan cobbled from haricot beans and almond essence; "eggs" that were tinned apricots fried in bacon fat. I opened one book, and realised with a horrible gulp that I was looking at advice for cooking crow. "Boil it up with suet," said the writer, "to keep the meat as white as possible." There was a recipe for sparrow pie too – though the Ministry of Food did not "encourage" the eating of these tiny birds.

David was abroad for the duration of the war. A restless and independent young woman – after St Clare's Private School for Ladies in Tunbridge Wells, she'd tried unsuccessfully to become an actress, and had briefly worked as a junior sales assistant at the fashion company, House of Worth – in early 1939, she and her lover, Charles Gibson Cowan, had set sail for Greece in their boat, the Evelyn Hope. When war broke out, they were in the south of France, and it was in Antibes, where they wintered, that she met her mentor, the writer and traveller Norman Douglas (the sybaritic Douglas would be the single biggest human influence on David when it came to food). She and Cowan set sail again in the spring of 1940, a decision that led to a brief internment in Italy and the loss of their boat, which was impounded. For a time, they lived on Syros in the Cyclades, but when the Germans invaded Greece in 1941, they were forced to flee to Cairo. She spent the rest of the war in Egypt, and there she married Anthony David, an officer in the Indian army, though the relationship was doomed from the start, and did not last.

No wonder, then, that when she returned to Britain in 1946, she was so appalled by what she found; in Egypt, she and Suleiman, her servant, had wanted for nothing, foodwise. She had even been able to hold regular lunch parties, at which she served lavishly seasoned kebabs and ice-cream, churned in an ancient and noisy ice bucket. "She couldn't believe it," says Norman, of what she found back at home. "I think she was really upset: shocked, even." Having moved in with her pregnant sister (Anthony was by now back in India), David took over the shopping: "One day, I took back to her, among the broken biscuits and the tins of snoek … one pound of fresh tomatoes. As I took them out of my basket to show her, I saw that tears were tumbling down my sister's beautiful and normally serene face." Elizabeth asked Diana what on earth was wrong. "Sorry," came the reply. "It's just that I've been trying to buy fresh tomatoes for five years. And now it's you who've found them first."

The winter of 1946 was exceptionally harsh; the snow drifts were so deep the country's meagre coal supplies struggled to reach power stations, causing many to close down. By way of escape, David headed for a hotel in Ross-on-Wye with an old lover, George Lassalle. This establishment was fabulously warm: according to David's biographer, Artemis Cooper, a coal fire burned in its public rooms, and maids provided the beds with hot water bottles. But the food was beyond bad: insupportable, in David's view, even allowing for the shortages; she was overcome with a sense of "embattled rage that we should be asked – and should accept – the endurance of such cooking". To comfort herself, she scribbled down lists of the things she most missed: apricots, olives, butter, rice, lemons, almonds…. This, then, was how she first began to write. Her notes and recipes were an expression of her yearning, a way of assuaging something that was not homesickness exactly, but which must have felt a lot like it.

In 1949, she began writing a cookery column for Harper's Bazaar, and soon after this, her first recipe collection was sent out to publishers. At first, she received only rejection notices. But at John Lehmann Ltd her manuscript found its way into the hands of Julia Strachey, a niece of Lytton who was then working as a reader at the company. Strachey liked the book, especially its seeming extravagance; its commitment to ingredients that were impossible to buy. A Book of Mediterranean Food was, then, duly published by Lehmann in June 1950, with a cover and illustrations by John Minton. Among its pages were recipes for such exotic delights as moules marinières and spanakopita, bouillabaisse and brandade, boeuf en daube and dolmades. In her introduction, David quoted Marcel Boulestin, the French chef and cookery writer: "It is not really an exaggeration to say that peace and happiness begin, geographically, where garlic is used in cooking." In spite of this – in 1950, garlic was widely and sincerely feared by most British cooks – the reviews for the book were rather good.

And so David's career as Britain's greatest food writer began. She followed A Book of Mediterranean Food with French Country Cooking (1951), Italian Food (1954), Summer Cooking (1955) and the book for which she is still best remembered, French Provincial Cooking (1960). She also continued to work as a journalist, at Vogue and at the Spectator. All the same, it was some time before her name was widely known. Hardbacks were prohibitively expensive; only when Penguin began to publish her in paperback did her work become more accessible (Summer Cooking was the first). Even then, her influence was limited to cognoscenti – intellectual and metropolitan. David, remember, was a woman who chose to cook – the granddaughter of a viscount, she had grown up in a house with staff - and as such, her work appealed to the upper middle classes rather than to the massed ranks of housewives in their new Formica-filled kitchens. Among her admirers, after all, was Evelyn Waugh. Certainly, she was an evangelist for olive oil, good bread and seasonal eating, but her writing, like her manner, could be patrician. It is important to remember, too, that cookbooks speak more loudly of our aspirations than our daily lives. David's ideas were only felt fully in the 1960s and 70s, which was when regular families like mine – and yours, probably – began tentatively eating such things as lasagne and avocados.

In 1965, she opened a shop, Elizabeth David Limited, in Pimlico, London, where she sold Le Creuset pans and other hard-to-get-hold-of kit. The store, with its marvellous window displays, was as influential as her books would eventually be, pioneering a new generation of shops devoted exclusively to kitchenware. But it was also a business disaster, and she severed her links with it in 1973. Thereafter, she devoted herself to a more scholarly kind of writing: English Bread and Yeast Cookery was published in 1977, and Harvest of the Cold Months: the Social History of Ice and Ices appeared posthumously, in 1994. She became a vociferous critic both of the supermarkets, and of the 80s "foodie" culture as satirised in The Official Foodie Handbook by Ann Barr and Paul Levy, a volume she loathed ("To be sure they are skilful enough in the arts of toadying to their public and providing it with a little giggle at itself, but the meaning of satire in the true sense eludes them," she wrote in her review for Tatler).

Towards the end of her life, she was famously irascible. She drank too much, too – frustrated by her inability to get around, and perhaps a little lonely: since her affair with Peter Higgins, the dedicatee of French Provincial Cooking, had ended in 1963, she had been single. The death in 1986 of her sister, Felicite, with whom she shared her house, was a terrible blow, plunging her into depression. But she was also able to see, by this point, that others would carry the torch she had passed to them: Jane Grigson, Jeremy Round (until his early death in 1989, David had hoped Round would write her biography), Simon Hopkinson. And others felt it, too, this passing of the baton. Her work would not be undone. Among the baskets of lilies, blue iris and violets at her funeral at St Peter ad Vincula in Folkington, East Sussex, on 28 May 1992, someone placed a loaf of bread, and a bunch of herbs tied up in brown paper.

I've read both biographies of David (the authorised volume by Artemis Cooper, and the unauthorised version by Lisa Chaney), not to mention most of her own books. Yet mysteries remain. Why did food, of all things, became so important to her? In some ways, she was so austere, abstemious even. Her passion for Nescafé and Roka biscuits seems more of a piece with her personality than a vast bowl of osso buco. And to what degree is she still an influence on the way we cook? Does the Jamie Oliver generation even know her name? I wonder, too, about her personality. Cooper makes her sound perfectly terrifying, but what kind of cook doesn't care for other people? Isn't the whole point of food – particularly David's kind of food – that it is to be shared?

"If she were about to join us now, I'd be feeling a combination of concern and enthusiasm," says her nephew Johnny Grey, a kitchen designer, with a mournful laugh. "I hate this portrayal of her as a drunken, cross person, but I would be quite nervous, yes." For a time, he and his aunt fell out. About three days before she died, though, they talked. "She held my hand, and she said: 'I want you to know that I love you.' I was, perhaps, her honorary son. Certainly no one else in the family had the connection with her that I did." So is he able to answer my questions? "Well, you're right about the importance of food in her life. I'm still pondering that one myself. She was quite an ascetic person. Not at all greedy. She must have had her sensual side, but we didn't talk about sex, and her affairs were illicit anyway. The nearest I've got to an answer is to say that food conjured up other times, other places." He pauses. "But even that's shrouded. If she was longing for the sun, why didn't she go and live in Europe? Why did she live in a damp, dark house in Chelsea? Her last kitchen was in the basement. I think it must have been that she didn't want to be an expat, to be identified with that kind of posh, idle person."

He remembers David as quite shy and modest. It was a pleasure to cook for her, or with her (she required guests, seated at her kitchen table, to perform various tasks). She could be hilarious, when she put her mind to it. Rosi Hanson, who worked in David's shop for two years, agrees. "People say she was difficult, but I didn't find that. She was the sort of person you wanted to please. We worshipped the ground she walked on. We wanted to be around her. She was good fun, and the shop was magical. She rather loved being a shopkeeper, perhaps because it gave her a rest from writing. If someone wanted some very specific piece of equipment, I often heard her say: 'If you could come back, I think I may have one at home.' On evenings when we stayed late to do the windows, she would make a picnic for us all to eat: terrine, things in jelly. Fantastic. If it was your birthday, she would give you a recipe, typed out." She rifles through a drawer, and pulls out several of these precious documents. One is for loin of pork spiced with green peppercorns. "A most original and subtly spiced dish," it begins. Floating beside it, in ink, are the words: "For Rosemary, with love from ED." Were recipients meant to try these recipes? "Oh, yes. But if something didn't work, she never admonished you. She was interested. She wanted to know why."

I ask Norman, who looks after David's estate, how she sees the legacy of her "beautiful, elegant, reserved, witty" friend (we have this conversation, incidentally, at a table that once stood in David's house in Halsey Street: a pine affair bleached pale with years of use). "I remember Prue Leith telling me that at a catering college soon after Elizabeth's death, she asked students how many of them had read her, and not a single one raised a hand. Prue was quite shaken. But the books do sell – I see the royalty statements – and you see her influence in the cooking of Jeremy Lee, Shaun Hill and Rowley Leigh. I think she would have loved the food at restaurants such as Moro and Ottolenghi. Towards the end of her life, she did get a bit bitter and cross, but she had reason. Fiddling about with food, over-garnishing; she hated that. She felt there was too much bad food about – the way the English made pizzas, she was always complaining about that – and some of the things on television, she would have been scornful. Elizabeth never, ever promoted herself."

All these conversations are interesting, and vivid in the telling. In the end, though, you can only go back to the books, to David's stern, crystalline prose – "I was once present at a learned discussion between two stubborn gentlemen, who were arguing as to the respective merits of the snails of Bourgogne and of those of Provence … simply absurd" – and to the recipes themselves, as familiar and as cheering as old pop songs, if a good deal more useful. They will always be with us. They mark a turning point in British food, it's true, but they talk to the present, too, and the future. Some things are unimprovable, and the best of her recipes are exactly that. Norman says the one she uses most often is the daube de boeuf, "which works for everybody and is so good". Grey loves her way with courgettes (grated, to be made into fritters) and her gratin dauphinois. Hanson points me in the direction of snow cheese, a confection made from double cream, sugar, lemon and egg white that should ideally be served in a heart-shaped porcelain dish as once sold by Elizabeth David Ltd. For myself, I will take the recipe for champignons à la grecque, as it appears in Summer Cooking – an oily and delicious dish of my childhood, when my parents, in their flares and cheesecloth shirts, first began experimenting with "foreign food". Even as I type I can feel the coriander seeds crunching delightfully between my teeth.

To order Rachel Cooke's Her Brilliant Career: Ten Extraordinary Women of the Fifties for £14.99 go to guardianbookshop.co.uk or call 0330 333 6846