The celebrated London restaurateur and judge on the BBC's latest food show, Great British Menu, was enjoying a Bank Holiday weekend meal with his wife and two young children during a short break in Cornwall.
Mr Peyton, 44, is an ardent supporter of the time-honoured Sunday roast, and the latest high-profile culinary figure to lend his support to The Independent on Sunday's Sunday Lunch Campaign.
The charismatic "gastropreneur" - behind famous London restaurants such as Mash, Inn the Park, in St James's Park, and the recently opened National Dining Rooms, at the National Gallery - said that Sunday lunch was an important national institution which should not be allowed to die.
"The Sunday meal, to us, is a sacred thing; it's the main time we all get together," said Mr Peyton, who has two children, Finn, four, and Molly, three. "For me, weekend meals are the time when we communicate with family and close friends.
"It's not just about the eating; it's about spending time together. It's a bond thing. Family-and-friends time is like a bubble, and everything else is outside that. It's soothing and it's therapeutic, and for me it's pivotal to how we live our lives."
Mr Peyton, whose wife - Charlie Polizzi, daughter of the hotelier and Forte heiress Olga Polizzi - is Italian, believes Britons could benefit from a more European approach to weekend eating.
"We've got lots of lessons to learn from the Italians and the French," he said, gazing out over the rock pools beneath the hotel terrace where his children have been exploring.
"Sunday lunch should be a big occasion. If you eat at home in Italy, they're much more concerned with the conversation rather than the preparation. Sitting down to have a meal is part of who they are in Italy, and that's where we've got to get to in Britain.
"I don't think getting together is just about opening a tin of beans and burning a piece of toast," he said. "It's the being together, and it keeps us together. We like the kids to be involved in the making of the lunch, particularly the pudding - the problem is keeping enough to eat at the end."
As recently as a generation ago, British families sat together for a meal nearly every day, but today a quarter of us don't even have a dining table. Only 12 per cent of people now say that they cook meals from scratch, down from 39 per cent just 10 years ago.
Mr Peyton is currently appearing on television as a judge on Great British Menu, which started airing last week on BBC2. Over the course of a two-month competition, some of Britain's top chefs will compete to cook a dish for the Queen's 80th birthday. The programme places heavy emphasis on regional British produce and cooking - something Mr Peyton believes could also hold the key to the revival of the Sunday lunch. "The fact that people are considering regional British food is a great thing - it's a stepping stone to the future because it gets people thinking about what's available to them" said Mr Peyton, whose lunch at Hotel Tresanton in the village of St Mawes consisted of Cornish vegetables and beef from the local butcher.
"The way people eat is a lot to do with what's produced around them. I do think a lot of the problem is a lack of respect for what comes out of the ground. People have become used to instant food. More good-quality produce in the regions means more people will become interested in cooking."
Mr Peyton said part of the problem could be the formal nature of British restaurants. "One of the problems in Britain is that restaurants are seen as places that are a bit too formal. In Italy, there are many restaurants where families can go and eat well. In Britain, there's a bit of pomposity about going to restaurants still. Good restaurants should be accessibly priced for family outings."
Another problem is lack of time. "The pace that people have lived their lives in recent years hasn't lent itself to communal eating," said Mr Peyton. "We need to get back to that."
Mr Peyton joins a growing list of supporters from the culinary world who have backed The Independent on Sunday's Sunday lunch campaign since its launch in February. They include Heston Blumenthal, Michel Roux, Antony Worrall Thompson, Jean-Christophe Novelli, Hugh Fearnley-Whittingstall and Brian Turner.
The IoS campaign is also supported by experts from Childline, Relate and leading hospitals.
What's the secret of getting the family around the table for Sunday lunch? Each month, we will publish a selection of your letters with a mouth-watering prize for the best one. Write to: Sunday Lunch Campaign, The Independent on Sunday, 191 Marsh Wall, London E14 9RS, or send an email (Subject: Sunday lunch) to: firstname.lastname@example.org
LUNCH WITH THE PEYTONS (Hotel Tresanton, St Mawes, Cornwall)
Cornish asparagus with hollandaise sauce. Local squid served with basil mayonnaise and organic salad leaves
Locally sourced beef fillet with crispy potatoes, Puy lentils, leeks and porcini mushrooms
Apple crumble with Cornish clotted cream
Four 200g portions of organic beef fillet
For the lentils:
150g Puy lentils
1 medium carrot
1 medium leek
1 medium onion
500ml chicken stock
For the crispy potatoes:
4 medium Maris Pipers (peeled, washed and diced)
Salt and pepper
16 baby leeks (washed and cleaned)
200g of porcini mushrooms
METHOD Cook the vegetables in olive oil until soft. Add the lentils and cover with chicken stock and simmer until cooked. Season the lentils with salt and pepper and a splash of balsamic vinegar.
Bring potatoes to the boil in salted water and strain. Place on a roasting tray with butter, salt and pepper and roast until crispy.
Season the beef fillet and seal the meat evenly in a hot frying pan. Cook to desired degree and allow to rest. In the same pan sauté the sliced porcini mushrooms until golden.
Steam the baby leeks until tender. Remove from water and roll in butter.
Arrange on the plate and serve.
Good on you, IoS. Families seem to spend a lot of time claiming to be there for each other, 100 per cent, 24/7, and all the other pious lies about genuine, interpersonal support. Rarely is it demonstrated. Eating together without distraction respects the food and the participants. It's a start.
JACK HUGHES, Brixham, Devon
Four generations regularly gathered round my table on Sundays. They learned the appropriate accompaniments - red currant jelly with lamb, etc. And some courtesy, passing dishes to each other in turn and speaking loudly and clearly to my 95-year-old aunt, still a good trencherwoman. Conversation, with my son practising as a nurse in an operating theatre, and my grandson and his housemate eyeing the female talent at local nightclubs, was never dull.
KATE TAYLOR, Wakefield, West Yorkshire
My daughter-in-law comes from Slovakia; I was surprised to learn that her family has no tradition of shared mealtimes except for festivals such as Christmas. Whenever her parents visit us they love to have the traditional Sunday roast with Yorkshire-ski puddings, as they call them, and home-made puddings, followed by the great British tradition of a leisurely stroll to work up an appetite for afternoon tea.
JANE CHITTENDEN, Norwich
In my late teenage years, Sunday lunch became especially important to me. Slightly hung-over, up too late for breakfast, ravenously hungry, I remember the mouth-watering, frustrating wait while the house filled up with the smell of roasting meat.
When I finally moved away to university, I carried on the tradition with one of my housemates. Because we were impoverished students, we weren't able to afford to buy the joint of meat, so Sunday lunch consisted of everything except the meat - roast potatoes, cauliflower cheese, mashed swede and carrots, Yorkshire puddings, and I have to admit, Bisto gravy, as we didn't have the meat juices to make proper gravy!
CAROL-ANNE HODGSON, New Malden, Surrey