The radio host repeatedly asked Angela Rayner for a figure to attain a cost on how much the initiative would cost.
Labour leader Jeremy Corbyn announced he wants to extend free meals to all primary school pupils in England, stating he would cover the cost by introducing VAT on private school fees.
But the Independent Schools Council said the “sums do not add up” and Ms Rayner struggled to put her finger on a number.
Speaking on his LBC show, Ferrari accused the Labour shadow minister of having “no idea” on the number of kitchens that would need to be installed.
Nick Ferrari took the shadow education secretary to task over Labour's free school meals pledge
After she could not respond to the radio host, Ferrari said: "You come out with this flagship policy, every primary school child in the land will have a meal, which is obviously eye-catching for parents, and then you're asked a question, 'well how many schools will have to put kitchens in?' and you actually have no idea do you?"
To which Ms Rayner responded: “You’re not listening to my answer. In 2020, when this policy is introduced as part of our manifesto, there are some schools that won't need a specific kitchen within their facility because they will already have the facility by the use of the next door school all the provision, so it's not a simple percentage.
“It depends on what the provision is currently within those schools."
But the LBC host hit back: "Don't you think it would have been an idea to know. Wouldn't it be an idea to say, 'We'll also have to commit – I'm going to make a figure up here – £100million to build kitchens in approximately 15 per cent of schools have no kitchen facilities.'
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"Because all we have at the moment is every child is going to have a free school meal. That's fantastic. What about is there a kitchen? No idea, haven't got a clue. That's the reality of what we’re hearing.
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“I’m going to quote that's reality what we're hearing. Unless there's a neighbouring school that can heat up Cornish pasty."
Speaking on talkRADIO, the host was baffled at the Labour party’s suggestion to place 20 per cent VAT on private schools in order to fund free meals for all children – including those from privileged backgrounds.
Hartley-Brewer picked the proposal apart as she suggested highly-paid individuals, like Ms Rayner, should not expect lower-earning people to pay for their children’s meals.