Conservative Party leadership candidate Boris Johnson gestures as he talks during the launch of his campaign in London, June 12, 2019.

The race to succeed Theresa May as leader of the ruling Conservative Party and prime minister entered a new phase on Thursday with Tory members of parliament (MPs) having their first vote for their preferred candidate.

Three of the 10 candidates standing in the leadership contest were eliminated from the race Thursday after failing to get the required backing of at least 17 colleagues in secret ballots; they were Andrea Leadsom, Esther McVey and Mark Harper.

The favorite to win the leadership race, Boris Johnson, got 114 votes. His nearest rival, Jeremy Hunt, got 43 votes. Environment Secretary Michael Gove got 37 votes.

The process of elimination will continue until there are only two candidates left, then the wider Conservative Party membership in a run-off vote to elect one candidate as party leader and prime minister. The next round of vote takes place on Tuesday, June 18. Candidates will then need at least 33 votes to proceed to the next round of balloting

A winner is expected to be announced on July 22.

Brexit, and how the various leadership hopefuls would progress the thorny departure from the EU, has dominated the debate in the run up to the first vote.

Party members, and the wider public, are keen to know how the next prime minister will fare any better than Theresa May did at uniting a divided Parliament behind a Brexit deal that it has already rejected three times. The EU too has already said it will not re-negotiate the deal.

The U.K. is meant to leave the EU on October 31 and with no deal agreed by Parliament, the prospect of a potential "no-deal" departure has returned to the fore.

As such, a lot of attention has been put on the favorite to win the leadership race Boris Johnson, the former foreign secretary and mayor of London. Launching his leadership campaign on Wednesday, he said he was "not aiming for a no-deal outcome" but said it was responsible to "prepare vigorously" for such an outcome. He said any more delay to Brexit would mean "defeat."

On Wednesday, the opposition Labour Party led an attempt to make sure the future prime minister could not push through a "no-deal" Brexit but failed to gain enough votes.