Former London mayor Boris Johnson is a step closer to becoming Britain’s next prime minister, winning 40 per cent of votes in the second round of a contest on a firm promise to leave the EU by October 31.

Johnson, the face of the official Brexit campaign in the 2016 referendum, won 126 out of 313 votes and goes through to a third ballot today with four other candidates who won 33 votes or more.

The former foreign minister was far ahead of the rest of the pack, stretching a lead which, for many, makes Johnson the all-but-inevitable victor to replace Prime Minister Theresa May.

At a sometimes ill-tempered BBC debate, Johnson repeated his pledge that he would take Britain out of the EU by October 31.

He said the only way to do so was to prepare for a so-called no-deal exit and concentrate on winning a new trade deal.

“We must come out on the 31st of October because, otherwise I am afraid we face a catastrophic loss of confidence in politics,” Johnson said.

“October 31 is eminently feasible. Let me just say if we now say that we have a deadline that is not a deadline and we allow October 31 to come and go as March came and went and April came and went, I think the public will look upon us with increasing mystification.”

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With Johnson so far ahead, the race is on for second place, with Foreign Secretary Jeremy Hunt, Environment Secretary Michael Gove, International Development Secretary Rory Stewart and Home Secretary Sajid Javid all trying to prove they would be his toughest challenger.

At a sometimes ill-tempered BBC debate, Johnson repeated his pledge that he would take Britain out of the EU by October 31. (PA/AAP)

Former UK foreign minister Boris Johnson is far ahead of the rest of the pack in votes for the next Prime Minister. (PA/AAP)

The remaining five will now face votes until the race is whittled down to two candidates, who will face a postal ballot of the Conservative Party’s largely pro-Brexit members.

A new prime minister should be chosen by the end of July.

At the debate, the four other candidates – after former Brexit minister Dominic Raab was knocked out – tried to test Johnson, who has so far been relatively silent in the campaign, even avoiding an earlier debate.

Johnson was taken to task for past comments in which he offended Muslims, women and others.

“In so far as my words have given offence over the last 20 or 30 years when I’ve been a journalist and people have taken those words out of my articles and escalated them … of course I am sorry for the offence they have caused,” he said.