Former British Foreign Minister Boris Johnson has stepped up the race to succeed British Prime Minister Teresa Mae after the results of the second round of conservative vote.

Johnson, 55, won 126 votes out of 313 during the second round of voting to elect a leader of the Conservative Party and the British government.

In contrast, Dominique Rapp, who served briefly as minister of the affairs of the BRIC, was unable to get 33 votes, the minimum set for the third round of voting on Wednesday. The remaining five candidates will compete in televised debates.

All 313 MPs are eligible to vote in secret to replace alternative Prime Minister Teresa Mae.

Other rounds will be held to reduce the list until only two are left, one elected by all the party's 160,000 members.

The winner is expected to be announced on 22 July.

The outcome of the battle for leadership could determine the conditions under which Britain would pull out of the EU on October 31 as scheduled.

Johnson said he was open to the prospect of Britain withdrawing from the bloc without formal agreement between the two sides, although he said he would prefer an agreement before the deadline.

Opponents of the pullout without an accord say it would cause economic chaos because the EU is Britain's most important trade partner.