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Kemi Badenoch and Bridget Phillipson were today involved in a heated Commons clash when the Conservative leader called the education secretary a “spiteful class warrior”.

Ms Phillipson accused the Tory leader of having “lost her head” after a behind-the-scenes incident following Prime Minister’s Questions.

The row was triggered during Ms Badenoch’s regular exchange with Sir Keir Starmer, when she criticised the education secretary over the ending of tax breaks for independent schools.

Ms Phillipson shook her head as Ms Badenoch said she “taxed private schools to pay for more teachers but the number of teachers has gone down”.

“It turns out appointing a spiteful class warrior as education secretary was a disaster,” the Conservative leader said, suggesting Sir Keir had been “let down by her incompetence”.

Sir Keir defended Ms Phillipson, saying she “grew up in poverty” and was an “incredible story of social mobility and success”.

Phillipson under fire

After the ill-tempered Prime Minister’s Questions exchanges, technology secretary Liz Kendall and Ms Phillipson were involved in a further incident with the Tory leader.

Ms Kendall is understood to have told Ms Badenoch that what she said was outrageous, as the trio met in the division lobby.

A Conservative source said Ms Badenoch responded by telling the education secretary: “I’ll fight you all the way. You’re destroying children’s lives” - a reference to the imposition of VAT on private school fees.

Other sources suggested Ms Badenoch told Ms Phillipson: “You are spiteful. I’m never going to stop talking about how spiteful you are”.

Ms Phillipson is understood to have told the Tory leader: “The public are going to find out who you really are.”

On social media following the spat, Ms Phillipson wrote: “Kemi lost her head at PMQs - and afterwards too.

“It’s not the first time. She’s compared me to a Gestapo officer.

“I wonder what it is about a working-class woman driving record investment in state schools by ending private schools’ tax breaks that the Tories hate so much.”