This is probably the first and, I hope, the last breaded turkey dinosaur to come out of a Jamie Oliver kitchen. My fork hovers over the dun-coloured monstrosity which Nora, the dinner lady, has placed before me. Do I really have to eat this?

I think about declaring an allergy to turkeys, or dinosaurs, or both. I think about running away. The last time I saw one of these was at a children's petting zoo on my two-year-old's plate. He turned his nose up at it, and rightly so. The turkey dinosaur is only food because eating one will not kill you, at least not immediately.

I was so appalled by it, so outraged, that I was immediately moved to take my son to the Michelin-starred Fat Duck in Bray to eat cuttlefish cannelloni, sea bass in a vanilla sauce and white chocolate with caviare. Partly I wanted to make it up to him, but mostly I wanted to prove that children have much more adventurous palates than the manufacturers of breaded bloody turkey bloody dinosaurs would want you to believe.

Jamie Oliver is trying to do exactly the same thing, but on a larger scale.

Alongside the turkey dinosaur (turkey content: 30 per cent. The rest is fat, breadcrumb, fat, salt and fat), there are baked beans and potato faces, which smile up at me with what I hope is the rictus grin of the condemned. They are, after all, yesterday's men, placed in front of me only so I can see what used to be on the menu in Greenwich, south-east London. I am going to taste three dishes from Oliver's new menu, which runs on a three-week cycle.

Admittedly, the setting is not authentic. It is half term so, instead of sitting in a school dining hall, I am at the chef's funky offices, at a bar by an open kitchen.

But Nora Sands is the real thing, a dinner lady from Kidbrooke School in Greenwich with 15 years' experience. She remembers the days of the Inner London Education Authority, when fresh meat and vegetables used to come into her kitchens every day. Then the catering was put out to tender. Profit margins withered and the unholy double act of Bernard Matthews and McCain's were allowed to reign supreme.

Today the budget per child is 37p and it's been 37p for the past five years. Oliver not only had to produce real food for 37p; he had to produce real food for 37p that the kids would actually want to eat.

'I didn't think it could be done,' Nora says. 'I was the worst sceptic in the world.'

If my tasting was anything to go by, though, it has been done, and how: first up, a plate of rice with a vegetable curry. I find it a little bland, but you can taste the fresh spice mixes that have been used and there are solid pieces of cauliflower and butternut squash in there.

But will the kids eat it? 'They love it,' Nora says. On the side is a cucumber and mint salad in a yoghurt dressing which, to use Oliver's argot, is 'zingy'. The rice is also slightly al dente, just as it should be.

Next up, 'Hot and Kickin' chicken': a whole chicken leg, roasted to a sticky crispness and flavoured with a marinade of chilli, cumin and paprika.

This time I can believe the children like it. But I can't believe the price. Can they really do this for 37p? In fact, according to the costing sheet, it comes in at 23p a leg. So no, it's not from some free-range, organic bird that was massaged with aroma therapy oils every day and slaughtered to the soothing tones of Vivaldi, but it is good quality chicken. And it tastes very nice indeed.

Finally, a slow-cooked balsamic beef stew, in a rich poky sauce, spiked with Worcester sauce. It's solid and sustaining. 'That's my favourite,' Nora says. I can see why. It's mine, too.

Alongside is a tomato and basil salad. As Nora is dressing it, I see her reach for a lovely carved bowl full of flaked sea salt. 'That's Maldon Sea Salt,' I say, 'Ten flakes of that and you'll break the budget.' Nora blushes. 'It looks like such lovely salt and I don't get to use that sort of thing.' She is handed the budget tub of Sainsbury's table salt.

Nora never used to use salt. 'We didn't season,' she says, 'and we didn't taste. Everything came out of a packet and was already seasoned.' A kitchen where nobody tastes? It sounds like the beginning of a very bad joke.

But it wasn't. The dinner ladies really cook now and that's one of the problems. If Nora's anything to go by, they love what they're doing but they are working longer hours for no extra pay. As the project has expanded to more than 25 Greenwich schools, the problem has become more obvious.

The team have negotiated their remarkable product costs using the clout of Jamie Oliver's name and the power of television. They have motivated people with an intense programme of training and a little celebrity stardust.

Oliver has started his 'half a quid a kid' campaign and argues that 50p a head isn't much to ask if we care about what our children eat. The government has responded with a bunch of guidelines on processed foods in schools but no extra money. Let's hope Oliver wins. It would be a tragedy if the breaded turkey dinosaurs were allowed to walk the Earth once more.