Nigel Slater got a shock when he invited Paul, Stella and Mary round to his place - he didn't really expect the most famous Beatle to make the dressing and clear the dishes

Sir Paul McCartney is standing in my kitchen making a dressing for the salad. We are discussing abstract artists. 'Look, I'll show you how to make a Jean Arp,' says Sir Paul, referring to the late French painter and poet, carefully dripping balsamic vinegar into the thick River Café olive oil and workaday mustard he has already put in the bowl.

'Dad, I've never seen you do this before,' says his daughter, the fashion designer Stella. As promised and right on cue, the glossy black vinegar makes a perfect Arp-like swirl against the canvas of the green oil.

'Oh my God, look, it is an Arp,' says his eldest daughter Mary excitedly, who decides, then and there, to photograph it.

'Hey guys, we are making salad-art,' says Paul, as photographer Mary clicks away.

'Dad's great at dressings, he always makes really good dressings,' says Stella.

'Mum was American, so salad has always been a big thing with us,' says Mary.

Paul McCartney stands in my kitchen and asks me for a lemon, slices it in half, squeezes it into his dressing by hand, dips in a finger, tastes it, adds a little more Maldon salt and black pepper from the mill, and whisks in some more oil. He knows exactly how he wants it to be, like he does it every day of his life. 'Am I making enough to do all that?' he says, pointing a thumb at the sink full of Fern Verrow's wacky organic leaves.

Fifteen minutes earlier, Paul and Stella McCartney walked through my front door, apologising for being (ever-so-slightly) late. Paul is wearing a black-and-white check suit, sandals and socks, Stella, a steel-grey Stella McCartney shirt that falls in soft waves from her shoulders. He looks relaxed and happy, despite his acrimonious split from his second wife Heather Mills - 'Hi Nigel' - while his daughter walks straight through to the kitchen and stands looking at the garden.

'Yes, we thought of having box hedging, too,' she says, looking at my rather bare kitchen garden, referring to her husband Alasdhair and their 250-acre Worcestershire farm, 'but I think we've decided not to now. Don't you have a problem with snails eating your veggies?' We discuss the fact that box hedging is, yes, the perfect hiding place for snails during the day, who then come out to party on your carefully nurtured organic lettuce as you sleep. 'I might do raised beds, but I don't really like those either,' she says, adding, 'I can't believe this, I'm talking about growing things all the time now.'

'I told you,' says her father, who has now joined us. 'It was the same with my dad, I never thought I would be interested in vegetables and stuff and he told me that one day I would. He was passionate about growing his own stuff.' I tell them both that an interest in gardening is a bit like wrinkles, in that it creeps up on you when aren't looking.

'What we having for lunch?' asks Paul, looking about 10 years younger than his 65 years, as he peers into a deep pot of furiously boiling water. 'I don't mind as long as it's not meat or fish.' I promise him it isn't.

Paul McCartney and his daughters Stella and Mary - who has been here for a while and has already made my day by noticing a much-loved photograph on the wall - are here to have lunch in honour of Linda, Paul's first wife and mother of both the girls. I tell him we are having the first asparagus from the Isle of Wight and then something of Linda's, some recipes from her cookbooks. I apologise for having tinkered with Linda's recipes a bit, wondering whether it might be like telling Sir Paul that I have just done a cover version of Revolver and missed out 'Yellow Submarine'.

'Oh, Mum would love that,' says Stella. 'She would be thrilled at the way things have moved on.'

'Linda was never precious about things. She didn't mind if people changed her recipes, in fact she loved it when they did,' agrees Paul.

'She never measured anything,' her daughters chorus.

Stella and Mary are excitable, and there is more than a bit of giggling going on; together they remind me of slightly naughty schoolgirls. Stella began her career at St Martins then became an intern at Christian Lacroix. Her rise to fame was assured when she took over from Karl Lagerfeld at Paris fashion house Chloé, and now has her own growing empire. They worked together on Madonna's wedding to Guy Ritchie: Stella designing the dress, Mary taking the wedding pictures. 'And when Mum was doing her books we acted as her sous chefs, doing all the chopping,' Mary adds. Between them, they look after me throughout our lunch, occasionally asking their dad questions that I forget, and constantly bringing my Dictaphone into the room when I am talking to him off-tape. 'I thought you might need this,' jokes Stella. They all help, carrying stuff in and out of the dining room, and at one point Paul follows me round with my tape recorder while we are laying the table and chatting. 'Hey look, I'm a Dictaphone roadie now,' he says, saving my bacon (so to speak).

The McCartneys talk about 'Mum' as if she is in the next room. It is as if she is still here, making the lunch, sending them to the local school, getting them to do the washing-up. 'You chop, you load, you wash, you dry,' she would say. She famously brought up her children, Heather by her first marriage, then Mary, Stella and the more reclusive James, like any other kids, eschewing fancy boarding schools and fabulously expensive presents in favour of a life more grounded and ordinary. But she later changed all their lives even more radically.

Already a respected professional photographer, Linda - daughter of lawyer Lee Eastman and Louise Linder Eastman, heir to the Linder department-store fortune - had arrived in London with a commission to take pictures of musicians and ended up committing the heinous crime of falling in love with every woman's favourite Beatle. They met at a Georgie Fame concert, going on to see Procol Harum at the Speakeasy Club before she flew back to New York, without even exchanging phone numbers. The couple were to meet again at the launch party for Sgt Pepper's and, yet again, in New York at a party for the Beatles' Apple record label. It was finally Paul who made the move and phoned to ask her to accompany him on a trip to Los Angeles. And it was Paul who would ask her, several times, to marry him. They married at Marylebone Registry Office on 12 March 1969, when she was four months pregnant with his daughter Mary. The same Mary whom Linda photographed tucked inside Paul's jacket for the cover of his first solo album, and who is now standing in my kitchen with a commission to photograph Linda's lunch.

We sit down to the asparagus, which, true to form, I manage to overcook. Stella and Paul studiously avoid the leather dining chairs, instead opting for the painfully creaky but more ethical vintage wooden ones. Mary and I sit on the ones made from dead animals.

'We were in the kitchen at the farm, sitting down to the usual roast Sunday lunch,' says Paul, explaining the family's route to strict vegetarianism, 'and through the window we could see all these little lambs, a great big gang of them, doing that cute thing that lambs do, you know, where they all run to one end of the field like this ...' He breaks off to do a lollopy impersonation of little lambs gambolling in a meadow ... 'And then they all ran back to the other end of the field. They were having a great time. And we just looked down at the leg of lamb on our plates. We made the connection and that was it. Linda picked up the ball. We decided then and there to give up eating meat.'

Linda had yet to become the much-liked figure she was to grow into and was then being given a hard time by the media, who attacked her trademark trainers and Argyle socks, not to mention her reputedly off-key singing with Paul's band, Wings. To add wood to their fire she had now turned our most famous rock star and his family into vegetarians.

'It wasn't like that at all,' says Stella, explaining her own vegetarianism. 'She didn't force it on us at all, it was a totally personal decision not to eat meat, not a family one.'

'Years later she credited me with saying that the family should go veggie,' continues Paul, ' but I don't want to take that credit.' We just saw the lambs in the field and Linda said, "Is there any way we don't have to eat this any more?" And that was the start of it.'

At that point, turning vegetarian wasn't a very rock'n'roll thing to do. Prior to Paul, Yehudi Menuhin was probably as near as vegetarianism had got to the music business (unlike now where vegetarianism and veganism seem almost as de rigueur as a spell in rehab). 'Yes, it was difficult, very difficult, but that moment gave us the passion. After the light bulb went on, we started to think of meat as the hole in the plate, and worked out how we could fill it.'

Filling the hole on the plate is exactly what Linda did, first for her family, then for the rest of the world, writing the fastest-selling vegetarian cookbook in history and going on to develop a line of innovative meat-free frozen suppers that, at one point, was selling 25 million units a year.

'Mum never minded when people copied her,' explains Mary, 'she just wanted more vegetarian food to be available for everyone.'

The arrival of Linda's cookbook in 1989 caused something of a storm. Published in the UK by the then fledgling publisher, Bloomsbury, Linda McCartney's Home Cooking sold 400,000 copies in its first few months. It is easy to forget how difficult it was for vegetarians in the Seventies, with little available for those who had no wish to eat meat. 'At first we were grateful when they brought us out a nut cutlet, but then ...' Paul trails off.

'A bit like it is in France now,' laughs Stella, who, like any non-meat eater, must find that country's somewhat backward attitude to the meat-free life deeply frustrating. Heaven knows how she eats during Paris Fashion Week.

Paul McCartney clears the table, brings the asparagus plates into the kitchen and stacks them neatly by the sink. Our main course is Linda's spinach pancakes stuffed with mushrooms, which I have chosen because they seem like a classic. 'So you just stir spinach purée into ordinary pancake batter, yeah?' asks Paul, who seems to not remember this particular recipe.

'Actually it was Linda's quiches I loved most,' he says, tucking into the soft green crêpes and doing battle with a slice of roasted organic pumpkin from Riverford Farm in Devon. 'They were fluffy and light and very, very rich. I'd never had quiche, it wasn't the sort of thing we grew up eating in Liverpool. Hers were big and lusty like a soufflé.'

'Yes, because you ate them straight out of the oven, Dad,' explains Stella, seemingly worried that her father's memory of his late wife's quiche is beginning to sound like he had eaten them under the influence of more than homegrown organic lettuce.

'No, they were really big and fluffy, even when they cooled and dropped,' continues Paul. 'I used to take great big thick slices of them to work the next day.'

We are all drinking water, with the exception of Paul, whom I have persuaded to drink a glass of the champagne I opened before they arrived. They explain that they never really do lunch - they are normally all too busy working. Drinking seems a bit of a no-no. Stella is still breast-feeding her daughter, Bailey. She has made the decision to bring up her son, Miller, who is two-and-a-half, without meat. 'He is the best-fed kid I know, he eats everything he wants. I guess when he'll get to the age when he wants to try things it will be fine. The same as it was with me. I don't think you should push anything on to people.'

Paul, Mary and Stella are remembering that first veggie Christmas. There are shrieks of laughter as Paul tells of the infamous Macaroni Turkey - 'a great thick macaroni cheese that we made and allowed to set, then we cut off slices and fried them up.

'It allowed me to do the masculine thing I had always done, to stand there and carve the roast.' While Stella and Mary remember the pasta turkey with their heads in their hands, Paul insists it was really good. One gets the feeling they have all moved on a bit from that one.

Linda is probably best known for her work as an animal-rights campaigner; her seminal collection of rock-star portraits, Linda McCartney's Sixties: Portrait of an Era; and her line of frozen ready meals; but the family agrees the food side has been in the doldrums of late. Recently sold by Heinz to Hain Celestial, one of the biggest names in organic and natural food, the range is now undergoing a facelift.

'We are relaunching them,' says Paul, animatedly. 'We have great new people involved and have reformulated them. We are really excited about them again.'

I ask Paul if the family is doing all this perhaps because he had made a promise to Linda, who died of cancer nine years ago this month. 'Yes, but it was an unspoken promise. She wanted it to continue, she was clear about that and the whole family was kind of part of it. We had all done the tastings together and were equally as proud as she was that we had helped to kickstart the vegetarian food market in Britain. We were one of the first, along with Craig Sams of the Soil Association and his brother Greg.'

'She started the whole frozen-veggie food thing and hoped that it would take care of itself,' interjects Mary. 'We want to continue her food values. Mum's kitchen was the heart of the home for the family and we used to hang out there and chat while she cooked, and it just feels natural to continue. Relaunching her food line is a natural progression of what Mum was doing.'

Linda first contracted breast cancer in 1995, and after an operation later that year appeared back on the road to good health, appearing at Stella's first major show, sitting at her husband's side. Then her doctors found that cancer had spread to her liver. Linda died on 17 April 1998.

'We just wanted to continue Mum's legacy,' explains Stella. 'We wanted to put some new energy into it, a re-evaluation of what Mum did. It has been really exciting to give it all a big kick up the arse.' Stella is a strict vegetarian and campaigner for Peta (People for the Ethical Treatment of Animals) to the point where her hugely successful fashion empire uses no leather or fur.

'I make shoes without leather for ethical reasons, because of my own beliefs, but I love it when someone comes in and buys something not simply because it's an ethically product but just because they like it. It's the same with Mum's food - it's not so much that this is veggie food, but that it is delicious food that just happens to be meat-free.'

I mention that they had once begged Paul and Linda to allow them to eat meat. 'Yes, it was on holiday in Jamaica, at a beach barbecue,' interrupts Paul. 'The kids were running around the way kids do and came up and pestered us to let them eat some chicken from the barbecue.'

Stella takes up the story: 'It's like a memory that you can't really believe. It's like a dream that one day I got to eat chicken.'

'Yes, and when you wake up you won't remember you ever ate chicken at all,' jokes Mary, getting all a bit Derren Brown.

Paul interjects: 'We told them they could try some if they wanted to, but they had to remember that they are the same birds that are running around on the farm at home. Remember that's what you are eating. Luckily, when you came back you said you didn't like it.' Stella also admits to a bit of a tuna habit when she was younger. 'Then I thought, "Why I am eating this? I believe in why I don't eat meat and I don't want to eat dead fish". So I stopped.'

Paul McCartney, Stella and Mary bring through the dirty plates and pile them on the kitchen counter. I ask them if they want some cheesecake. For some time now, I have felt as if Linda was in the room. It must be the easy way they talk about her, as if she is still here. I unmould the cheesecake, secretly worrying that the recipe of cream, cream cheese and blueberries won't hold up without a bit of gelatine and will collapse over the kitchen floor. It doesn't. Thank you Linda. There is much excitement as the cheesecake is brought into the room, its pale, milk-white surface now dripping with richly purple blueberry sauce.

'Hey, and this is Linda's, too?' asks Paul. I have to explain that I followed her recipe for redcurrant cheesecake but substituted blueberries instead because of the time of year and because it is easier to find organic blueberries than redcurrants. 'Hey, you put ginger in it too,' cries Paul as he digs in. 'That's exactly what she would have done to move the thing on.' We sink our spoons into the soft, creamy cake. 'It is because we like animals, it's an ethical thing, not really about health,' explains Paul. Which is just as well considering the amount of fat in this particular treat. 'This is so illegal!' giggle Stella and Mary.

It is only then that I notice just how fit and healthy the three of them look. I look at their radiance and their slight other-worldliness and note how the whole house has been full of energy and laughter since the second they crossed the threshold. They remind me of what I have noticed over the years, that people who don't eat meat always seem to look younger than those of us who do.

Stella, whose cruelty-free beauty range, Care, hits the stores this month, is adamant. 'I don't understand why humans think they are better than other animals on the planet. These are animals we should be living in harmony with. Why do we think we have the right to eat them? As Mum said, "It's sea life, who the hell are we to turn it into sea food?"'

All four of us lost our mothers when we were young. Paul when he was 14, and me when I was nine. Linda was diagnosed in 1995 after a routine scan, and despite an operation and a long and painful course of chemotherapy, her cancer was to return. By that time she had won over her critics and, I hope, shamed the vicious interviewers who seemed at one point to knife her at every turn. She had seen Mary's photographs accepted into the National Gallery, Stella's meteoric rise to become the coolest designer working today, and Paul become the most successful songwriter in history.

I admit to having turned to food as my comfort after my own mum died and in particular to dairy produce. 'It's the breastmilk thing, my personal theory that we are trying to replicate the ultimate comfort,' I suggest, and then we are off on the subject of comfort-eating - wave after wave of greedy chatter and saturated fat.

Stella says she wants to be vegan but loves the comfort of cheese too much; Paul is remembering his mother's Yorkshire pudding which they always ate for dessert, with treacle; Mary admits 'When I was really depressed, I had grilled cheese, fries and ice-cream and I felt so much better afterwards. Look, I know I'm meant to be having my omega 3, 6 and 9, but a tub of ice cream makes me feel fabulous.' For Paul, there is much comfort, too, in mashed potato. 'I make mashed potatoes to die for, a little bit rich, you know.' His daughters wax lyrical about Dad's legendary mash to the point where I am ready to ask for the recipe, mash being a thumb I occasionally suck, too.

We are finishing up our cheesecake. I've eaten the filling but have left some of the base; Mary has eaten the base and left a little of the filling; Paul has eaten both. I ask how it was that Linda went from being media whipping boy to being so universally loved and respected, suspecting a bit of a PR job.

'You know what, people just gradually got to know her. They came to stay and people ate her food and listened to her,' says Paul. 'We had a discussion about whether we ought to do stuff together, for me to introduce her to the public and then we thought, "Sod it. We will just carry on as normal."'

'You went to live on a remote farm in Scotland Dad!' cried Stella, sounding as if they had run away to Venus or Mars.

'We said sod that, we don't have to justify our relationship, if that meant that people didn't know about her, but they slowly got to know her, she did her cookbooks and people started to understand what she was about.'

People got to see how tirelessly Linda McCartney campaigned against cruelty to animals, (she was a patron of the League Against Cruel Sports) and they saw how, even after she was ill, she used her influence to push vegetarianism forward. It is probably partly due to Linda that vegetarians no longer have to constantly explain themselves every time they sit down to eat.

'It wasn't really about her changing people's perception of her, it was just about the animals,' continues Paul. 'She didn't really mind what people thought.'

'You know, she would sometimes put on pink and orange nail varnish at the same time, just to please herself,' says Mary, wistfully. 'She put crystals on the window because she liked the rainbow effect it made on the wall.'

That the family has remained vegetarian for so long means that they are in the perfect position to continue Linda's business interests, keeping her range of frozen food at the forefront, carrying on her legacy.

The organic side of things used to be a headache. In the early days they just couldn't source enough organic ingredients, but now, more than a decade on, they are finding it easier to get hold of it in the quantities they need. I point out that at the end of the day it is still a frozen convenience meal for one. 'Yes,' says Mary, 'we are talking about frozen food here, which can be quite depressing when you walk down the aisles, so it was important to make it a bit more life-enhancing. Mum felt that cooking was a very tactile and sensuous thing to do, and we wanted to get that message through with the new packaging.'

Paul likes the new range of Linda's food. 'The past few days I've been on my own at home. I've been cooking for myself and I just took some of the new products, steamed some veggies and made a salad to go with them. It was a really good test.'

Paul McCartney stands in my hallway and asks if he can borrow a plate. 'I want to take a piece of this cheesecake to Steve Jobs at Apple,' he says. And then he leaves, a piece of Linda's gorgeous cheesecake in his hand, continuing Linda's legacy.

Linda McCartney's pancakes and cheescake recipes

Spinach pancakes with mushrooms

Serves 4

125g plain flour

sea salt and freshly ground black pepper

1 free-range egg, beaten

300ml skimmed or soya milk

175g cooked spinach, thoroughly drained

vegetable oil

25g margarine

625g mushrooms, sliced thinly

3 large cloves garlic, crushed

25g plain flour

75ml skimmed or soya milk

grated nutmeg

125g mozzarella cheese, diced

parsley to garnish

Sift the flour and seasonings in the blender, add the egg and milk, blend until smooth. Add the spinach and blend again. Thin if necessary with more milk.

Brush a 20cm frying pan with oil, heat it, then add 2 ladles-full of the pancake batter. Spread it to cover the bottom of the pan evenly. Cook the pancake for 1 minute before turning to brown on the other side. Keep it warm while you cook the remaining pancakes. Heat the margarine in another pan and cook the mushrooms with the garlic for 3-4 minutes or until the juices run. Stir in the flour to soak them up, then gradually add the milk a little at a time, stirring so the sauce is smooth. Season to taste with salt, pepper and nutmeg. Fill the pancakes with the mushroom mixture, roll them up and place in baking dish. Scatter the mozzarella over the top and bake at 180C/ 350F/gas 4 for 15 minutes. Serve hot garnished with parsley.

Redcurrant cheesecake

Other seasonal soft fruits in season can be used.

Serves 6-8

175g digestive biscuits

50g margarine, melted

1kg low-fat soft cheese

175g light soft brown sugar

300ml double cream, whipped

250g redcurrants or preferred seasonal fruit

Crumble the biscuits finely. Add the margarine and mix thoroughly. Press evenly over the bottom of a greased 20cm loose-bottomed flan tin. Chill until set. Beat the soft cheese with the sugar until creamy. Fold in the whipped cream, then fold in the fruit. Pile on to the prepared base and smooth the surface. Chill for several hours before serving.

Taken from Linda's Kitchen (Little ,Brown)

· The Linda McCartney range of 11 dishes is now available in most major supermarkets, ranging from £1.59-£1.99