(Bloomberg) -- Theresa May faces a showdown with her cabinet on Tuesday as she seeks their backing for one last push for her divorce deal with the European Union.

Pro-Brexit ministers and those looking to succeed May as prime minister are expected to lead objections as they debate proposals to make the agreement more attractive to the opposition Labour Party, potentially including a much tighter customs relationship with the bloc.

May said she will put the Withdrawal Agreement Bill -- which enshrines the Brexit deal into law -- to a vote in Parliament in the week of June 3 and is trying to find a way to get it passed. Formal talks with Labour broke down Friday, but she is seeking to win over enough of the party’s lawmakers to get her deal over the line.

The failure of the talks and May’s pledge to set a timetable for her departure increases the risk of a no-deal split from the European Union as Tory MPs jockey to succeed her. To lead the party they will need the support of party members, 66% of whom support leaving the bloc without an agreement while only 27% back May’s deal, according to a YouGov survey of 858 Tory members between May 10 and 16.

The pound fell more than 2% last week as May announced she would set a timetable for her departure and it appeared her successor would be likely to push for a harder split from the EU.

Brexiteer Boris Johnson, a pivotal figure in the 2016 referendum campaign, is the current favorite to replace May, and polls show he would win a vote among party members. But first the former foreign secretary, who wants a quick, clean Brexit, will have to secure the backing of MPs to be one of the two candidates voted on by rank-and-file party members.

The Times newspaper reported that Chancellor of the Exchequer Philip Hammond will use a speech Tuesday to attack leadership front-runners Johnson and former Brexit Secretary Dominic Raab for being prepared to accept a no-deal divorce.

“There is a real risk of a new prime minister abandoning the search for a deal and shifting towards seeking a damaging no-deal exit as a matter of policy,” Hammond will say, according to the paper. He intends to continue to fight for a negotiated exit because “we have an absolute obligation to protect Britain’s jobs, businesses and future prosperity.”

’Contingency Plan’

A group of Tory MPs, including cabinet ministers David Gauke and Amber Rudd, launched a caucus in Parliament on Monday evening that is pledged to pursue economic and social responsibility through “one nation Conservatism.”

While as a group they stopped short of committing to oppose the election of a party leader who favors a "no-deal" split, Rudd said it should only be seen as a “contingency plan” in case other options fail.

“Any new candidate is going to have to measure their Brexit policy against our values,” Rudd told BBC TV’s “Newsnight” show. “No-deal Brexit is there in case it happens, but very much at the center of government policy is getting a deal and that’s what I -- and most of us in the group -- would look for in a candidate.”

The Conservative Party suspended Michael Heseltine from the party in the House of Lords on Monday evening after he said he would vote Liberal Democrat in Thursday’s European Parliament elections to oppose the “self-harm” of Brexit.

“On this issue, the transcending issue of our times, I need to stand up and be counted,” Heseltine, who was a cabinet minister in the administrations of Margaret Thatcher and John Major, told Sky News. “They can take away the whip, but they can’t take away my integrity, my convictions or my experience.”

To contact the reporter on this story: Thomas Penny in London at tpenny@bloomberg.net

To contact the editors responsible for this story: Tim Ross at tross54@bloomberg.net, Robert Jameson

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