Nick Clegg has been taken to task over his free school meal policy by a caller claiming to be a nine-year old boy, who told the deputy prime minister the results were not very impressive.

The Liberal Democrat leader was interrogated on his LBC 97.3 Call Clegg show by someone who gave his name as Rohan, from a school in south London. It came in the week schools were forced to provide free lunchtime meals for all four- to seven-year olds.

While Clegg claims all schools are prepared to deliver the meals, some headteachers have complained they have had to cover some of the costs by raiding other budgets and installing new kitchens. The caller was so eloquent that some questioned whether Clegg had been stitched up by a political opponent pretending to be a child.

Rohan told Clegg that his old school had been forced to dine in the gym, meaning pupils could not do their usual activities there at lunchtime. The purported nine-year-old also said the free lunches at his school were unhealthy and questioned the evidence for the policy, saying improvements for pupils were not very big.

The deputy prime minister initially appeared bemused by the child's questions, asking him whether he should be at school. But Clegg went on to defend the policy, saying all the evidence shows that it is "extremely helpful in the schools where this has been introduced in the past.

"Not only does it save mums and dads money, about £400 a year to pay for the lunchtime costs, it's not only good for your health because – I'm sure this is not the case for you, Rohan, but quite a lot of children go to school with lunchboxes which don't have very healthy food in them."

Clegg continued: "I don't know, a slice of white bread with some chocolate spread and a fizzy drink, where it is better to have a proper cooked hot, healthy meal with vegetables and so on, but actually, the schools where they've done this they've shown that the children who eat healthily at lunchtime, because they can concentrate better in classes in the afternoon, do better at English and maths than children who don't."

Rohan asked why free lunches could not be targeted just at poorer families or less wealthy areas of the country. Clegg said: "There are about four in 10 children in our country who are categorised as being poor – by the way, you really should go into politics, you're one of the most articulate nine-year-olds I've ever come across – there are lots and lots of children, four in 10 children who are poor, who the government says are in poverty, don't receive free school meals.

"There aren't just certain areas of the country where there are poor children who don't receive free school meals, they're everywhere and as I said the evidence is that if you really want a class to do well having children share a meal together, healthy meal together at lunchtime, so everybody, if you like, starts the classes in the afternoon with the same energy, that has a dramatic benefit."

Rohan would not, however, let Clegg off the hook, saying: "Surely, couldn't you spend some of that money on another project? Because I have seen the evidence and it wasn't very big, the percentage point increase – it was only 1.9 in one of the trials. And also it was bigger for key stage 2, than key stage 1."

Clegg asked the young caller where he had got his information from, suggesting an adult had helped him. But Rohan said he had researched the subject on his own, via the internet at home.

When asked what he had for lunch yesterday, Rohan said: "Brown bread sandwiches with minestrone soup, with beans in it and some vegetables, and salad on the side."

At one point in the interview, what seemed to be a school bell could be heard in the background and, at the end, Clegg suggested the caller should "probably go back to class".