Angela Rayner said the move would help children aged 5-8 who get “lost in the system” and others with behavioural problems “get the education they deserve”.
She also claimed some schoolchildren’s education was suffering from learning in class sizes of up to 40.
But Rayner failed four times to answer a question from LBC’s Nick Ferrari about how many schoolchildren the policy would help.
“Do you not think it would be a good idea to have a sense of how many people you’re talking about?” Ferrari challenged her. “You are the Shadow Education Secretary.”
In the days after Diane Abbott was skewered for her maths on extra police numbers funding, Rayner held her own when quizzed by the same presenter.
“There’s quite a substantial amount of pupils that are affected,” she said. “I haven’t got the numbers on me to hand, but it is quite a substantial amount of children that are in class sizes that are over 30.”
Despite the repeated questioning, Rayner maintained she was not going to “pluck a number out of thin air”.
Ferrari hit back: “I’m not asking you to pluck a number out of thin air. One of your key pledges is to try to reduce class sizes - which will really resonate with my listeners - for 4, 5, 6 and 7-year-olds.
“I’m asking you how many this will affect and all you can tell me is it is a substantial number? Shall I help you? I’ve got a number - shall I give it to you?”
Ferrari claimed the figure was 520,445, prompting Rayner to respond: “I told you it was a sizeable chunk Nick, and you had that number so you knew exactly what I was talking about.
“We’ve been absolutely clear about that. I’m just not going to play that numbers game with you and pluck one out of the air.”
Labour later clarified to HuffPost UK that it expected 538,254 children - slightly more than Ferrari claimed - to benefit from the policy.
Rayner’s performance received a mixed review on social media.
Rayner was doing the media round as her leader launched the party’s education manifesto.
As well as cutting class sizes for under-8s, the radical £20 billion education shake-up contains a plan to reverse planned tax breaks for big business and instead spend the money on a new National Education Service for young and old.
Maintenance grants for students would be restored and a new scheme for free, lifelong skills training would be introduced, he pledged at the policy launch in Leeds.