The BBC is planning a Question Time programme with the final two candidates, which could include one-to-one interviews with Andrew Neil.
Speaking about Tuesday night's debate, a friend of Sajid Javid told the Telegraph: "It wasn't an edifying format and if they want to make a pitch for another TV debate you would want it to be a bit more thought through.
"It will play into our thinking as to whether we agree or don't agree to another BBC event. ITV, Sky and Channel 4 all want to do a head to head as well and the Channel 4 debate on Sunday was very well done.”
A source close to Jeremy Hunt said: "We are reserving judgement but it's fair to say we didn't think it was brilliant."
Another source close to Boris Johnson told the Telegraph: “It hasn't helped the BBC's case for hosting a Question Time-style debate.”
It also emerged after Tuesday night’s debate that Mr Patel also had posted a graphic showing Israel being relocated inside America as a “solution for Israel-Palestine conflict” – the same one that Labour MP Naz Shah shared in 2016, leading to her being briefly suspended from the party.
An earlier version of this article stated that Mr Patel had tweeted that he had "consulted the Muslim Council of Britain and Islamist advocacy group MEND ahead of his BBC appearance". This was incorrect, and we apologise for the error
