Foraging is very now. On trend and magnificently seasonal, all you need is a pair of gumboots, a set of Kilner jars, and the time and inclination to preserve everything you see. There's wine out there, and gin, and beer, soups, salads and soufflés – a whole great Waitrose of stuff all just waiting to be turned into chutney.

"Everyone," says one wild food expert glumly, "is making jam this year."

So why, when it all sounds such fun, should the cities be left behind? The challenge is therefore to feed myself for a week from what I can find in the royal parks, the public squares and the two best-known cemeteries – Brompton and Kensal Green. I'm not allowed to use Hampstead Heath, Wimbledon Common or Richmond Park, and most of the canal towpath is off-limits. Whatever I forage has to be the main ingredient to any dish, but can be supplemented with shop-bought extras (sugar for jelly etc). It's going to be interesting; I am neither an expert forager nor a good cook.

DAY ONE

At the moment, it is not the threat of either starvation or poisoning that bothers me, but lack of coffee. Acorns are probably the best-known natural substitute but are universally considered disgusting. Still, if I want a cup of coffee without standing by the Starbucks' bins and begging, acorns it is. I gather up a couple of handfuls from Hyde Park, take them home, spend a remarkably long time peeling, chopping, roasting and grinding them, and then stick the kettle on. The resulting brew looks like coffee and smells nicely nutty. And to my astonishment, it's OK. It doesn't taste anything like coffee and it helps to add a bit of sugar, but it's not half as vile as I thought it was going to be.

I set off northwards in search of dinner. In Primrose Hill, under Macclesfield Bridge, I find a few brambles, some rosehips and elderberry. Further on there are what looks like wild strawberries. Wild strawberries are the nectar of the Gods, the best fruit ever invented. These look right – right leaves, right colour, right size. Wrong time of year, though. And these are weird-looking – neat and fat and sprayed with little red pips in ruthlessly tidy rows. I pick one, inspect it and (ignoring all good foraging advice) eat it. It tastes like mattress stuffing.

In Old St Pancras graveyard, directly below the new Eurostar line, there is a patch of waste ground full of yarrow, nettles, and plantain. I pick the cleanest examples I can find and keep going past the plum trees of Judd Street (too high) to the squares of Bloomsbury. In Tavistock Square the branches part and a squirrel the size of an African baboon descends, its mouth so stuffed with walnut it can't even manage the usual armpit-chucking up-yours gesture of the true WC1 Grey before vanishing into a bush.

Back at home, it is late and I am hungry. There's the crab apples to turn into jelly, the rosehips to boil, six or seven plants to try to identify, and nettle soup to look forward to. Three hours later, I have identified the bionic red thing at Gloucester Gate as a mock strawberry – evolution's idea of a practical joke. I also have three jars of crab apple jelly, one pan of carbonised rosehips, an inedible plum crumble and absolutely no idea what the hairy serrated leaf which smells strongly of parsnips might be. Finally, in a filthy temper, I produce some sort of soup from the nettles and plantain, stuff half of it in and go to bed.

DAY TWO

Breakfast is the Macclesfield Bridge brambles and elderberries with a bit of sugar. They're a bit tart – not the rich heady berries of August, but thinner and more astringent. Elderberry is supposed to be good for treating some types of influenza; shortly afterwards, it becomes evident they have other uses as well. Something I've eaten is working very efficiently as both emetic and purgative. Neither of foraging's two key texts, Roger Phillips's Wild Food and Richard Mabey's Food for Free, mentions any problems with elder. But urgent internet research yields the information that the raw berries, like the rest of the plant, contain traces of cyanide. Magnificent. Day Two and I'm going to die.

In between the time spent not-dying and the bits feeling queasy, I do further research. Turns out there's a far more exciting life in London's parks than I'd imagined – even conkers can be dangerous. Conkers contain acetone, a component in cordite, the main propellant in first world war artillery shells.

By now it is midday, and since I haven't yet joined cyanide's undistinguished list of victims (Goering, Hitler, Rasputin) I head towards Hyde Park, where I spot several sweet chestnut trees covered in bright-green furry burrs. Most of those on the ground aren't open yet, but there's something thrilling about spotting the fattest husks. This is a genuine treasure hunt – if I can find a couple of handfuls, then I'm in business.

Past the endless private squares of Earls Court to Brompton Cemetery. Here among the gothic crosses and the cruisers flitting coyly between the colonnades, there is plenty to be found. As well as the beautiful but poisonous yews there is an amazing range of plants and trees, some of which (like the vine entwining itself round an urn) must once have been graveside plantings. I collect a handful of ground elder, crab apples and a few more sweet chestnuts.

The legality of foraging like this is not entirely clear-cut. Brompton Cemetery is covered by the same set of regulations as the royal parks. They say only that no one should "interfere with" any plant or fungus or do anything to damage the wildlife. Fishing with a permit is allowed in certain areas, though you have to put your catch back.

I'm picking nettle shoots with an old pocket knife when the security guard comes round to close up for the night. I assume he's going to stop me, but instead he watches what I'm doing. "Can I make a suggestion?" he says. "Don't use that knife." Why? "This place is crawling with undercover police. Get yourself a pair of scissors instead."

Oh, I say, OK, thanks. But why the police? "Dealers," he says, pointing to CCTV cameras. "Rough sleepers, muggers. Bad people hang out here."

Back at home I stick the rosehips and crab apples on to boil and follow Roger Phillips's recipe for chestnut soup. Boiling and peeling the chestnuts is a bit fiddly, but the rest is easy enough. The result is, according to everyone else, "excellent".

DAY THREE

I cheat. The yellow crab apple jelly goes fine on toast, even if that toast is (mumble) bought. In theory, crab apple jelly is supposed to go with meat, but in practice this week is turning out vegan. Various carnivorous suggestions have been offered – feral pigeons, squirrels, snails, urban foxes, Serpentine geese, ring-necked parakeets, small dogs – but none is particularly tempting. Besides, I don't have the means to kill them. Poisoning and trapping are presumably illegal, archery and fish-tickling could be tricky, and somehow I suspect that brandishing a firearm round Whitehall or Buckingham Palace might turn this from a piece on foraging into a first-hand examination of the criminal justice system.

Instead, I spend part of the day down on my knees by the ladies' loo in Regent's Park trying to hook an ornamental quince. There's a low-growing shrub behind the railings covered in interesting-looking yellow things, though I can only get hold of them with a bit of low cunning and a loose interpretation of the words "interfere with". Some have already fallen and others can be grabbed with the handle of an umbrella.

Regent's Park has a productive history. During the second world war, the eastern side of the park was turned into allotments as part of the Dig For Victory campaign. Even now it is still being used to produce food. Toby Mason has more than 30 separate beehives on five separate sites in the park, all screened from public view by brambles and fencing.

Bees, he says, are endlessly absorbing. "I love it. I can always find an excuse to be here, to check on them, top up their food, find out how they're flying. It's more or less a full-time job." The resulting honey is a lovely pale-golden colour and tastes of lavender and lime blossom – Mason sells it through posh grocer Melrose and Morgan in Primrose Hill. But while quinces and honey may be fantastic, they don't add up to dinner. A night off is necessary; we eat out.

DAY FOUR

According to various sources, there are still a few old walnut trees left in the City: one in Lincoln's Inn Fields, one down near St Paul's, and one in Whittington Square, named after the four-time Lord Mayor of London who gave the city its first 148-seater public convenience. The paving below it is black with sap from the abandoned husks, but there's nothing left – the squirrels have pilfered the lot.

Back at home I contemplate the day's haul. Even when combined with a handful of ornamental lemons gleaned from St Paul's churchyard and enough herbal tea ingredients to start a women's group, three-and-a-half walnuts does not constitute a satisfactory afternoon's work. Dinner therefore involves a challenging reinterpretation of culinary norms: Weed Soup on a bed of Crab Jam, followed by Crab Jam on Weed Soup.

DAY FIVE

Just past the Amy Winehouse lookalikes at Camden Lock, Paul Haddow sits in a chair by the canal. Beside him is a small pot of breadcrumbs, a landing net and a long fishing rod from which the line hangs slack. The day is bright, and the water is a thick brackish green. What's he trying to catch? "Carp, bream, tench, roach, perch. Could be anything. Perch has stripes on it, roach is a silver fish, carp are massive – 30lb sometimes." Can you eat any of them? He stares. "You're having a laugh, incha?" He looks down at the water. "Would you eat something out of here?" Er, no. "Well, then. There's Eastern Europeans and all that come down here. They eat what they catch, but no one else does."

I leave him to it and head west. Along the road at Carlton Vale, I finally find what I've been looking for. London is stuffed with fruit trees, gnarly old branches freckled with apples hanging tantalisingly over garden fences, but that's the trouble – they're all private. There aren't many public fruit trees in Zone 1 but here, planted on a new estate, is a series of beautiful apple trees. I ask the neighbours if they mind me taking the windfalls. The apples are more ornamental than useful – even the young ones are woolly – but combined with the quinces, they should be fine.

A couple of days later I meet professional forager Fergus Drennan. Drennan is best known as the Roadkill Chef, though more recently he's been busy trying to live off only what he could forage from the Kentish countryside. Disappointingly for him and reassuringly for me, he was forced to abandon the experiment after a few months, defeated by the sheer impossibility of earning both dinner and a living at the same time.

Today he's telling stories in the Chelsea Physic Garden. Foraging in cities, says Drennan, should really be the same as foraging anywhere. The difference is that each part of the countryside – woodland, salt marsh, riverbank – will be home to different plants, but in the city everything will be muddled up together, so you've got to know your way around. "But in cities the hazards are the same – misidentification; pollutants, whether they're natural, like dogs, cats, foxes or people peeing on plants, or pesticides and herbicides. And if your identification skills aren't up to scratch, there's all sorts of introduced species and ornamentals that could trip you up."

We leave as the staff lock up for the night. Drennan takes a few ginkgo berries and then hands me what must be the most exclusive foragings in London: five beefsteak tomatoes from the Physic Garden allotment, a grapefruit, a pomegranate, five windfall quinces and a chilli pepper, plus two huge bagfuls of dried chestnuts and walnuts he'd brought along in the belief that I was halfway to starvation. The tomatoes get turned into salad, the quinces and grapefruit into jelly and fool, and the chestnuts into flour for bread. Finally I have a full meal – a true feast.

And so, at the end of this highly unscientific experiment, I've learned several interesting things.

1. It is not possible to live solely off what you can forage from central London. I got through the week mainly by cheating, and by dispensing with lunch completely.

2. Foraging for yourself takes an astounding amount of time; foraging for two or more people is a full-time job. This is why human civilisation took so long – everyone was out looking for lunch.

3. Foraging definitely hones one's book-reviewing skills. Never mind Austen or AM Homes – no book will change your life quite like a wild food guide with a few typos. For this reason, stick to the printed editions and be wary of online sites.

4. Foraging has its own private codes: don't take more than you need, don't damage or uproot anything, stick to very common species and windfalls. Nothing is more likely to make you aware of a plant – its texture, its smell, its seasons and properties – than either growing it yourself or finding it, and nothing will make you honour the food you eat more than properly needing it.

5. And finally, foraging will also take you on a whistle-stop tour of London's finest cruising sites. It's an interesting fact that the places that foragers go for (parks, trees, greenery, waste ground) are also beloved of those who like their sex al fresco. In theory the two don't coincide, since foragers need daylight and cruisers prefer night. In practice the rustling in the shrubbery might well turn out to be hunter-gatherers of an entirely different kind. If you'd prefer not to mix with undercover Sun reporters hoping to catch George Michael in the act, then probably best to skip the west side of Hampstead Heath. OFM

Nettle soup

1 bag young nettles (about the size of a football)

2 or 3 potatoes

I large onion

1 or 2 cloves garlic

a splash of oil or a little butter, for frying

I litre chicken or veg stock (or water plus stock cube)

salt and pepper to taste

Wash and drain the nettles, and discard any thick stalks. Chop the potatoes, onions and garlic, and fry in oil or butter until onion is tender. Add the nettles and stir briefly. Add the stock. Bubble gently for 12 minutes or until the potatoes are soft. Liquidise, re-heat and adjust seasoning.

Elderflower water ice

100g sugar

750ml water

100g fresh or 25g dried elderflowers

juice of 2-3 lemons

In a heavy pan dissolve the sugar in the water and bring to the boil. Add the elderflowers tied in cheesecloth and boil for a few minutes. Remove pan from heat and cool. Remove the flowers and squeeze out excess liquid. Add the lemon juice and pour into a shallow freezing container. Freeze and stir every hour or so until it is set in a nice grainy mixture. Soften in the fridge before serving.

Crab apple jelly

2kg crab apples

1-1.5 litres water

granulated or preserving sugar

Wash and cut up the crab apples. Place in a preserving pan with water just to cover – about 1.2 litres. Bring to the boil, then simmer for about 1 hour. Stir occasionally and mash the apples once or twice to release the pectin. Ladle into a jelly bag and allow to drip for several hours. Strain and measure the juice into the rinsed pan. For each 500ml of juice add 450g sugar. Stir over a low heat until sugar is dissolved then boil for 40 minutes, skimming regularly. Pot quickly in heated jars – the jelly sets fast.

Adapted with thanks from Wild Food by Roger Phillips (Pan)