At 7.30pm on the night of the greatest storm of the winter, I sit down to dinner at L'Enclume, in Cartmel. Outside, it's mayhem: the trees are jerking wildly from side to side, like girls trying to squeeze into too-tight jeans; the beck has developed waves; the scaffolding on the medieval priory lists and creaks alarmingly. But inside, all is calm. The ebb and flow of service is as soothing as a cashmere blanket. In quick succession, I'm presented with the first of 21 courses: an oyster "pebble" hidden like treasure in a wooden box; a cow's heel, dehydrated to resemble a prawn cracker and served with curds and onion "ashes"; a "hot pot" that is really a beef consommé with three perfect meat and potato pearls floating inside it. There is a version of a prawn cocktail served in a pottery "sack" with mace powder and a massive dose of chutzpah; a cod and saffron "yolk" that comes with puffed rice and a miserable sense, once you've had the first mouthful, that it will be gone far too soon; and then, like a clean page, a plate of good, sweet bread made with local Cumbrian ale.

It's at this point, just as I'm spreading rendered pork fat thickly on to a warm roll, that it happens: the lights go out. In the pitch dark, the rattle of the windows seems louder than ever; when the rain hits the glass, the sound is of marbles falling on a tin tea tray. But the room itself is oddly quiet. No one cries out in disappointment, perhaps because their anxiety at such a prospect is so great. L'Enclume, which has two Michelin stars and the kind of reputation that turns even Porsche-driving plutocrats into reverent pilgrims, is booked up months ahead; it's also quite a journey, unless you happen to live in Grange-over-Sands. Those who have saved up for a visit, who have braved the West Coast Main Line or the M6, are hardly going to indulge in amateur dramatics now. They're going to cross their fingers and pray the kitchen has a generator out back.

A waiter appears, bearing venison with charcoal oil, mustard and fennel. "This is a tartare," he says. "And I promise that's not just because the electricity is off." At the other side of the room, another waiter is reassuring people that all is not lost. "We'll do our best," he says. "There may be some dishes we can't make if the electricity doesn't come back on, but we'll deal with that when it happens." Later, I will find out that one member of staff has already driven to Grange-over-Sands to pick up his mother's flambé kit, a relic from the 70s, and his Primus stove, just in case. "The show will go on," says the waiter.

The pace slows a little. It's a while before the arrival of the native lobster with black pudding, parsnip, and sour cream with roe and chives, and there follows quite a gap before the salt-baked beetroot, glazed ox tongue, yoghurt and apple marigold appears. Then, at 8.50pm, the lights come back on. No one cheers because no one wants to tempt fate. They want what's still to come – the monkfish with bread beer and triangular garlic, the suckling lop with pennywort, and the celeriac with sweet cheese and malt, a refreshing fizz of apple and Douglas fir served in a little stoneware bottle on the side – and I don't blame them. This is once-in-a-lifetime food: beautiful, unusual, singularly delicious. When the lights, after another brief blip, do stay on right until the moment a tiny Kendal mint cake ice-cream is delivered to me on a slab of Lakeland slate, the sense of relief is palpable. None of us will ever forget our dinner on this wild and windy night. But this would be the case even without the storms and the power cuts. It's the food we'll remember, not the darkness; the Yorkshire rhubarb with sorrel and brown butter, not the flickering candles and the howling gale.

Simon Rogan is chef-proprietor of L'Enclume, and his apparently preternatural calm in the face of the worst the weather can do bodes well for the coming months. In May, Rogan will take over from Gordon Ramsay at Claridge's, one of the great dining rooms of the world. The pressure will be intense. For one thing, Rogan, though acclaimed in the UK, is not yet an international name; Claridge's has taken a calculated risk by signing him, and he will need to repay its faith and investment quickly, and in spades. For another, he will run this new kitchen alongside his ventures at the Midland Hotel in Manchester, where he has two restaurants (The French and Mr Cooper's) and his empire in Cartmel (as well as L'Enclume, Rogan owns a more casual restaurant, Rogan & Co, and a pub, the Pig and Whistle). How is he going to keep his eye on everything? "Well, they're not in different countries," he says. "So that's the first thing. The Pig, Rogan & Co and Mr Cooper's will have to get by without me; it's about trusting my lieutenants there. That leaves me with L'Enclume, The French and Claridge's. I'll spend half the week in London. But when service finishes at about 10.30pm your adrenaline is still going. Chefs can't sleep until two in the morning, so when I'm finished in London, I might as well jump in the car and drive home." Claridge's will be his focus, but he is not about to start neglecting L'Enclume. "We've still to achieve a third Michelin star, which we want very much," he says.

Is he serious about driving to Cumbria at 2am? I believe he is. Of all the chefs I have interviewed – quite a number by now – Rogan is one of the more driven. Stubborn, restless and fiercely competitive, he dislikes criticism, and has in the past been prepared to fail rather than to take advice (this is his judgment, not mine). Though the call from Thomas Kochs, the general manager of Claridge's, came just hours before he was about to sign with another major hotel group for a London dining room, he found himself unable to say no.

"I'd heard bits and pieces through the grapevine," he says. "They were talking to René [Redzepi, of Noma in Copenhagen], and they were talking to Thomas Keller [of the French Laundry, in California]… I felt at the time that it should really go to a British chef, and I would still feel that now, even if it wasn't going to be me. But of course, it should be me!" He arrived at Claridge's to meet Kochs in full disguise – or at least, in a baseball cap and sunglasses – and they hit it off straight away. Soon after this, Kochs made a return visit to Cartmel. "Beautiful, artistic, unexpected, no repeats, no silliness," Kochs says, when I call him later for his side of the story. Kochs is – how to put this? – quite an effervescent man. But even by his standards, he sounds ecstatic. He decided to bet on Rogan, because he is the future. "We thought: how will people want to dine in the next 10 years? His philosophy connected to that. And Simon is right. It would have been just a little bit wrong if we had chosen a German or a French chef."

Where does Rogan's drive come from? "I'm 44," he says, as though this were part of it. "I've always wanted to achieve." But is there anything in his background that might have contributed towards it? Not really, though he began cooking early; his parents both worked, his father as fruit and vegetable wholesaler on Southampton market, his mother as a clerical assistant, and it was left to him to produce the family meal. "I loved it. I taught myself: roast dinners, spag bol, curries, cottage pie. At 13, I got a weekend job at a Greek restaurant. I earned £24 a week, and that was like being a millionaire at school. They took me on full-time at 16, when my dreams of being a footballer were beginning to fade." He was promoted to grill duties and sent on day release to catering college. "I turned up thinking I was the bee's knees, but all the others were working in good hotels in the New Forest, and I was actually absolutely rubbish and didn't know anything." This focused his mind. "I quit the job in the Greek restaurant, and went to a posh hotel myself. The chef had been at the Savoy, and he gave me a great classical grounding. Now I was earning no money at all, but that no longer mattered: I was head over heels in love with it. I wanted to get to the top, and that was 10 years of getting punched and battered and things thrown at me."

He worked in a variety of places; he spent eight years, for instance, with Jean-Christophe Novelli. But all the time, the feeling was growing: he wanted to work for himself, and to do something different. "I had a chef de partie who had worked for Marc Veyrat in the Alps, who was God to me [in his heyday, Veyrat, a practitioner of molecular gastronomy, had six Michelin stars and was considered by many to be the best chef in the world]. His use of Alpine wild herbs and flowers; that was what I wanted to do. I used to think so every time he talked about him."

In late 2002, he took a call from a recruitment consultant friend. Catering and Hotelkeeper had been in touch about some premises, an old forge, in Cumbria; the freeholders were having trouble renting it out. "I was looking for a restaurant, but not here. I was living in Littlehampton. It took me five weeks to come up. I had a look round, and the owners sold me their vision of how we would survive. I didn't believe them, of course. I didn't know where my customers were going to come from. All I knew was that it was a beautiful building, and that they would give me the tables and chairs of my choice." He hadn't been to Cartmel before; he'd barely been to Cumbria, so far as I can tell. But in the car on the way home, he put in his offer. How did this go down with his partner, Penny? "Badly. She was very much against. Our son was only a month old. It was a huge gamble. We had to sell our house, car, hi-fi, all our prize possessions. And for what? A restaurant in the middle of nowhere that was going to serve this avant-garde food."

For the next eight months, he experimented. "It was a fluke that I ended up here, but I soon realised I couldn't have landed anywhere better, given what I wanted to do: the pure air, the amazing ingredients." These days, L'Enclume is supplied almost entirely by a farm Rogan owns farther down the valley (it has expanded recently, the better to be able to supply Claridge's, too). But some crucial ingredients continue to be foraged, just as they were when he first arrived. "The first thing was the wild herbs and flowers," he says. "We started using lovage, calamint and elderflower – all quite unusual then – and our tasting menus grew from there." His vision was incredibly clear, right down to the way the room would look. L'Enclume has a kind of purity that makes you think of Scandinavia: whitewashed stone walls; handsome oak tables made by local craftsmen that are ever-so-slightly irregular in shape, like pebbles; stoneware plates from a local pottery; glasses made from recycled bottles by young offenders. It is as if Cranks had collided with Le Gavroche (I mean this as a compliment).

At first, it was tough. The restaurant was open for only half the week, and even then he struggled to fill it. "A busy night was 20 people, if we were lucky." Slowly, though, the word started to spread. In 2005, having banished foreign ingredients from his menu, Rogan picked up its first Michelin star (he was bleaching the grout in the shower of one of the restaurant's bedrooms when he heard the news). Ever since, its march has been relentless. In the 2014 Good Food Guide, it replaced Heston Blumenthal's Fat Duck as the best restaurant in Britain. The effect, both for Cartmel and for Cumbria, has been dramatic. Rogan's village empire has since attracted other businesses: a cheese shop, a microbrewery, a bakery. Meanwhile, L'Enclume is seen as a blueprint for just what a hyper-local restaurant can be. "People said we'd never be able to limit ourselves to cooking with only Cumbrian produce, or not in the winter. But we've done it, and now others are copying us, which is flattering when they're sincere. When they're just trying to rip us off, though, it's annoying."

At L'Enclume, his cooking is growing ever more simple. "It's a case of growing the perfect carrot rather than cooking it perfectly. My dream menu would serve 20 raw courses, but I know [he laughs] I'd never get away with that." He won't single out a favourite dish. "It's about the whole menu: the way it flows, the rhythm, the balance." Nor will he tell me much about the menu he is planning for Claridge's, save to admit that while most of his ingredients will continue to be British, he will permit the odd white truffle. "I won't be reinventing myself," he says. "They wanted me, not some new version of me." Is he nervous? "Not really. The eyes of the world will be watching, but that's why I'm there." He tells me that it irritates him greatly that L'Enclume still isn't spoken of in the same tones as, say, El Bulli used to be – a fact he attributes to its distance from London. "People still feel it's a ball ache to get here, and tourists who come to London are just too bloody lazy." But at Claridge's, they will have no excuse: the restaurant will be a taxi journey at most.

I'm sure he's right; doubtless some people do look at the map and think: no thanks. But more fool them. There's something magical about the journey to Cartmel: the proximity of mountains and sea; the silvery peninsula light; the sense, as you dip down into the valley, that your quest is at an end. After we finish speaking, I leave the restaurant, and head back to my room to change for dinner. It's a short walk, but the wind is building; I must push against it, right shoulder first, as if it were a barn door. As I do, I think of Rogan's forager (he employs one full-time). Was he on the fells today? Crikey, I hope not. Michelin stars apart, it's this, of course, that is Rogan's greatest achievement – the way his food connects you in some quite primal way to its source. Will he be able to pull off the same trick in the muffled, art deco splendour of Claridge's? His new masters must be praying that he will. For there's something wonderfully honest about this way of cooking, and salutary, too. The trick of it is that you simply cannot take it for granted. Gratitude is part of the deal.

Simon Rogan's new restaurant at Claridge's, London W1 opens in early May