Seven-thirty in the morning, and the deliveries are arriving: monkfish and octopus, courgette flowers, pak choi, mange tout and oyster mushrooms. But this is not a restaurant: it’s a school kitchen, though unlike any I’ve seen in my four children’s combined careers of roughly 55 years of eating school lunches. The person taking the deliveries is Nicole Pisani, former head chef at Nopi, Ottolenghi’s upscale West End restaurant, who now spends her days cooking for 500 primary school children.

Fewer than half of London’s students eat school lunches, even though numerous studies show the benefits to concentration and understanding of eating properly at lunchtime; almost 20 per cent of children are obese by the time they leave primary school; and research shows that only 1 per cent of packed lunches meet the nutritional standards that currently apply to school food.

Schools must provide food at lunchtimes. (For the first few years after the second world war, lunch was free for everyone: after 1950, schools started charging but, for the next 25 years, school dinners were nearly universal.) Today, in some parts of the country, schools fulfil their duty simply by providing a sandwich. But overall, it’s fair to say that school food has improved significantly since its low point in the 1990s, not least thanks to Jamie Oliver’s vehement disgust with the Turkey Twizzler. The requirement since 2014 to provide free school meals for all pupils in Reception to Year 2 has focused attention on what is being served to infants, while the inclusion of cooking in the National Curriculum up to the age of 14 has given schools a reason to think about food as something more than an inconvenient box to tick and never mind the refined carbohydrates, sugars and trans fats.

Gayhurst School, where Nicole Pisani has been running the kitchen for 18 months, is a red brick Victorian primary on the edge of London Fields in Hackney. A couple of generations ago, the surrounding houses were slums, or not far off; today, every other front door has a drift of wistaria dangling above it. The hipster parents dropping off infants have American, Italian and French accents as well as British. But the school has a number of estates in its catchment and 25 per cent of children receive the pupil pre­mium grant (high for Britain as a whole, although low for Hackney).

Illustration by Lucinda Rogers

Before Pisani arrived, Gayhurst’s food, as at many London schools, was bought in from an outside caterer. The one member of staff who has survived from that time admits she didn’t do much cooking. The food wasn’t appalling, according to Executive Head Teacher Louise Nichols, who oversees Gayhurst and two other Hackney schools, but it wasn’t great either. “Before I arrived, the children thought chicken nuggets were food,” Pisani says. “Now, if we have chicken, I know where it’s come from and how the chickens were kept, I know how long it’s been here and what spices I’ve used. Before, there were baked potatoes every day. Some children never ate anything else.”

Previous efforts to improve school food, Nichols notes, have focused on its nutrition but ignored infrastructure. Two years ago, when the cost of lunches at Gayhurst was running at £25,000 a year over budget, she wrote a job description for someone rather different from the usual school cook: a person who would have a vision for food in the school, including growing it and teaching about it.

It’s probably an understatement to say that she was very fortunate at this moment in having Henry Dimbleby as a parent and a governor. Dimbleby was then writing The School Food Plan for the Department for Education; his tweet about the opportunity at Gayhurst reached Nicole Pisani, who was then head chef at Nopi, and had previously worked at The Modern Pantry and Soho House.

Pisani is from Malta, but received most of her food education in London. “Food knowledge in London is brilliant,” she says. “When I first arrived at The Modern Pantry it was like a foreign language: ‘go and get some sea beet from the fridge.’” At Gayhurst she serves samphire and seaweed, although she notes that sometimes the children go on holiday for a week and come back with their old, fixed notions about what they want to eat. There are boxes of cardamom and cinnamon, sesame seeds and turmeric on the shelves; a big bunch of tarragon sits on top of a pile of peppers. One of her staff bakes bread every day: today it’s soda bread; another day it might be focaccia studded with cherry tomatoes and rosemary from the garden or Moroccan bread with figs.

Pisani has brought in her own suppliers, coordinating with the two other schools under Nichols’ jurisdiction to increase buying power: she is able to order for 2500 children. (The kitchen of one of the other schools is run by someone Pisani trained, the other by a former Masterchef quarter-finalist.) One problem she faces is that many of the best suppliers – Ottolenghi’s butcher, for example – are doing their restaurant runs in the centre of town first thing and she needs an early slot: service starts at midday.

The kitchen at Gayhurst is now responsible for more than simply putting food on lunch tables. Today, Pisani’s deputy, Cheryl-Lynn Booth, takes baby carrots, bright radishes, celery and courgette flowers over to the nursery block. One of the nursery teachers tells me that the head of his own children’s primary school in Bethnal Green has heard about what’s happening at Gayhurst: she wants a chef too. The children gather round Cheryl-Lynn to learn about which parts of plants can be eaten. They prefer roots (carrots) to stems (celery); Cheryl-Lynn takes away the courgette flowers to stuff them with feta and olives and herbs and will bring them back to try later, when they are cooked.

By making everything from scratch, even bread, by getting rid of waste and by wielding her purchasing power wisely, Pisani has got rid of the overspend. This year, Louise Nichols is expecting food costs to come in £12,000 under budget. The savings have all gone into staff. The job descriptions are now head chef, sous chef, chef de parti. Everyone is working longer hours. Previously, most of the kitchen staff worked between eight and 14 hours: now the average is 30. “Nicole had to adjust from restaurant HR to public sector HR,” Nichols says drily. “She was saying to me, ‘this person can’t cook and doesn’t want to learn, can’t you make them go away?’”

Pisani says that a lot of the people who worked with her at Nopi have asked for a job. “Restaurant hours are terrible: 60 hours a week, 90 if you’re running the kitchen. You forget all about weekends. People get tired.” The Gayhurst kitchen staff are much more highly skilled than the usual run of school cooks: they have knife skills, they work on a section, they bake bread, they must expect to have their food tasted and approved at the pass; they are expected to care about presentation and not simply slop food onto plates.

Today’s menu is burgers (including vegetarian burgers) – which, not surprisingly, are one of Pisani’s most popular dishes – with caramelised onions, sweetcorn with ginger, Chinese vegetables (kale, rainbow chard, pak choi, mange tout, oyster mushrooms – “they love it when you give things names,” she says), with, on the table, gherkins, cheese, smoked aubergine dip and flatbread, plus lettuce and cous cous salad. “They don’t love lettuce,” Pisani admits, “but we hope to get them to pick at it.” To follow, there is banana bread. It is all absolutely delicious.

As I leave, there is an octopus in the sink, waiting to be prepared for tomorrow. The school charges £1.75 a day for lunch, compared with the £3 charged by some other schools in the borough. “The Pupil Premium Grant children are outnumbered by the affluent children,” Nichols says, “but we’re all about shouting for them to do just as well. And it’s often the children in families that have no access to public funds who will go hungry if you don’t give them a meal.”

Yotam Ottolenghi has been to eat at Gayhurst; he and Henry Dimbleby have agreed to be trustees of Nichols’ and Pisani’s next scheme, a school kitchen, where children from Gayhurst and other schools can learn to cook. (The lack of teaching kitchens in primary schools makes meeting the new National Curriculum cookery requirements quite tricky.) The new kitchen will also be a place to train school chefs. They plan to crowdfund it. Pisani’s dream is to see a network of professional chefs in schools.

Meanwhile, Gayhurst was inspected two months ago. The school now has a international reputation for putting food at the centre of the curriculum: teachers have come from abroad to see how Nichols and Pisani are managing to cut supplier costs while serving lunches of monkfish kebabs. The Ofsted inspectors didn’t eat with the children and didn’t note anything in their reports about the herbs and vegetables growing in containers all over the playgrounds. In fact, they didn’t once mention food.