Nick Clegg has been taken to task live on radio over his free school meals policy by a listener claiming to be a nine-year-old child.

The deputy prime minister was answering questions on his LBC 97.3 Call Clegg show when the caller – referring to themselves as Rohan from south London – said the introduction of free school meals for all primary school pupils in England was flawed.

Speaking live on air, the listener said: ‘I was wondering why you have decided to introduce free school meals, which is a very expensive product and at my school they're quite unhealthy? The evidence shows that they don't make children behave or achieve better.’

Clegg was quick to defend the policy, which was launched earlier this week with a £1bn investment and £150m for councils and schools.

‘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 added: ‘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.’

However, Rohan insisted that many parents could already afford to pay for those meals and asked whether the deputy prime minister could instead target the policy to poorer areas.

Clegg responded: ‘Actually the children who benefit most are the children who are poor, who are not wealthy...’

Yet Rohan quickly jumped in, claiming many of those youngsters would already be entitled to free school meals.

Clegg admitted the caller was ‘one of the most articulate nine-year-olds I’ve ever come across’. He added that there are four-in-10 children who are poor that don’t receive school meals.

‘The evidence is that if you really want a class to do well, having children share a meal together, a 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,’ he said.

While many Twitter users questioned the legitimacy of the Rohan’s age, a spokesman for LBC Radio said: ‘The production team spoke to the boy and his mum, and we were confident the caller was genuine’.