(Bloomberg) -- Labour Party leader Jeremy Corbyn’s appeal to other U.K. parties that he should become a caretaker prime minister to stop a no-deal Brexit looks to have already fallen flat, as even some in his own party apparently accepted an alternative plan was needed.

Corbyn on Wednesday evening wrote to rival party leaders, as well as selected Conservative members of Parliament, and suggested they should support him to oust Boris Johnson so he could seek a delay to Britain’s departure from the European Union and call a general election.

While the Scottish National Party and Plaid Cymru, who between them have 39 MPs, expressed a willingness to discuss the idea, it was rejected by the Liberal Democrats, who have 14 MPs. The party’s leader, Jo Swinson, called Corbyn a “divisive” figure who had no realistic chance of getting a majority behind him even on a temporary basis.

“There’s no way he can unite rebel Conservatives and independents,” Swinson said in a speech in London. “It’s not even certain he could secure all the votes of Labour members of Parliament.”

Corbyn’s proposal was that he should table a confidence motion -- as leader of the main opposition party, he is the only person who can demand such a vote and be certain of the request being accepted -- once other parties had agreed to his plan.

Although Corbyn insisted on Thursday that it was his right to lead the administration that would follow -- Labour has 247 seats and would thus supply three-quarters of the votes behind any replacement government -- some MPs in his party seemed to acknowledge that he wouldn’t be a plausible candidate as a caretaker premier.

“If the PM loses a vote of no confidence, of course the Leader of the Opposition should be first in line to test the confidence of the House, followed by anyone else who seems to stand a chance of forming a government,” Chris Bryant, a Labour MP, said on Twitter. “There’s no reason not to have several attempts in short order.”

Stephen Kinnock, another Labour MP, told Politico that if lawmakers rejected Corbyn, it would be reasonable to ask him to support an alternative prime minister.

But Corbyn’s letter has largely highlighted the difficulties of a so-called government of national unity, a plan floated by some to stop the no-deal Brexit that they fear Johnson will otherwise pursue. He didn’t even write to the former Labour MPs who quit his party earlier this year. Given that their reason for leaving was his leadership, that makes sense -- but he would need their votes.

His letter also confirmed that he wouldn’t allow Labour MPs to support any other such caretaker government.

And Corbyn also revealed that his priority is a general election, rather than stopping Brexit altogether. Those who want to keep the U.K. in the EU prefer the idea of calling another referendum. While Labour is now committed to holding such a vote if it wins power, it has kept open the option of campaigning to leave the bloc.

The primary focus when Parliament returns next month is likely to be less on any confidence vote than in moves by the large group of Conservative MPs -- including former Chancellor of the Exchequer Philip Hammond -- to find a legislative route to blocking no-deal.

To contact the reporters on this story: Robert Hutton in London at rhutton1@bloomberg.net;Alex Morales in London at amorales2@bloomberg.net

To contact the editors responsible for this story: Tim Ross at tross54@bloomberg.net, Stuart Biggs, Mark Williams

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