The party was ahead of the ruling Conservatives according to a forecast for a TV company following Sunday’s election.
The Conservative leadership candidate said he wanted to abolish the centrally controlled candidate list system.
Tory MP Gagan Mohindra accused his party of not doing enough for children with special educational needs and disabilities (Send) while in power.
Robert Jenrick said that the party should be ‘firmly on the side of parents’ in the wake of Ms Badenoch’s interview.