Conservative leadership contender Dominic Raab has hit out at rival Boris Johnson, claiming the party did not need a leader so easily caricatured as being part of the “privileged elite”.

The former Brexit secretary made the comments as the race to become Britain’s next prime minister became increasingly bitter, ahead of a further round of voting among Tory MPs knocking out at least one rival.

It also comes as the candidates – with the exception of Mr Johnson – prepare for their first televised debate tomorrow on Channel 4, with the broadcaster expected to present viewers with an empty podium for the ex-foreign secretary.

Mocking the decision of the frontrunner to duck the debate on Sunday, Mr Raab told The Daily Telegraph: “Everyone is going to have to demonstrate that they have not just the vision but the nerve and mettle to deal with the EU and with a minority government.

“If you’re not up for the TV debates and the test that provides, people will argue it’s a barometer for what would happen if you get the job.

“If you can’t take the heat of the TV studios, what chance of taking the heat of the negotiating chamber in Brussels?”

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Mr Raab, who needs to add to his first-round tally of 27 votes to continue after the second round, also criticised Mr Johnson’s plans to cut taxes for around 3 million higher earners, by raising the 40p threshold from £50,000 to £80,000.

And he pitted his own personal background against Mr Johnson’s, contrasting his grammar-school education and upbringing as the son of a refugee with an ex-public school rival like the Old Etonian Mr Johnson.

He said: “Are we going to be in a better position to do that with a candidate who isn’t so easily caricatured as being from the privileged elite, with the son of a refugee, a grammar-school boy who is offering tax cuts to most of those people on £15,000 as opposed to people on £50,000 and above?

Frontrunner Mr Johnson will miss the Channel 4 debate on Sunday (EPA)

“What is the impact of that in a tight marginal race? It’s about energy and youth and also having a vision, but it’s also about the practical electoral reality of who is going to better-placed to win in seats where Conservatives ask: are they really on our side?”

Mr Raab’s remarks followed the decision of Matt Hancock, the health secretary, to drop out of the race after trailing in the first round of voting on Thursday with just 20 backers.

He declined to reveal which of the surviving candidates – Jeremy Hunt, Michael Gove, Dominic Raab, Sajid Javid, Rory Stewart and Mr Johnson – he would support.

Mr Hancock will “mull things over” in the coming days, The Independent was told, amid suggestions he will back Mr Javid as another “moderniser”.

The home secretary’s camp strongly denied rumours he will drop out as “b******s”, insisting he was just nine MPs short of the 33 votes required to clear the second round of voting on Tuesday.