Ex-Tory chancellor George Osborne has told cabinet ministers they have a “responsibility” to move against Theresa May in order to save the party from future electoral defeat.

Urging those hopeful of succeeding the prime minister in Downing Street, Mr Osborne said: “Fortune favours the brave in these leadership contests.”

It comes after Ms May appeared to defy growing pressure from Conservative MPs to speed up her resignation, and outline a departure date.

But Sir Graham Brady – the chairman of the 1922 committee of backbench Tory MPs – said on Wednesday the prime minister will address the 1922 executive next week amid frustration over Ms May’s position in the wake of the worst set of local election results for the party in a generation.

Speaking to Sky News, Mr Osborne said that eventually the Conservative Party will need to “confront the truth” that it needs a new leader.

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“It needs a new agenda,” he continued. “It needs to win over supporters who have disappeared from it and it needs to make an appeal to the urban, metropolitan Britain that has currently turned its back on conservatism.

“If that continues to be the trend, then there won’t be a Conservative government for much longer.”

Mr Osborne, who was famously sacked by Ms May in one of her first acts after taking power in 2016, added: “There is a point where you have to ask yourself how many more elections are we going to lose?

“We lost the majority in 2017, we got hammered in the local elections earlier this month and now we have got the European elections where it is possible that for the first time in its long and distinguished history the Conservative Party is going to come fourth in a national poll.

“Essentially, there is a responsibility on current MPs – and indeed the supporters in the country – to do something.

“It is within their hands. You can’t just say ‘it’s all beyond my control’. If you are a member of the cabinet, you have a responsibility.”

He also said Jeremy Corbyn’s incentive was not to “rescue” the prime minister in cross-party Brexit talks but to replace her in Downing Street, adding: “I don’t know how much longer the Conservative Party will give her but I would find it extremely odd if we got to the Conservative Party conference and there was still Theresa May giving the leader’s speech.

“I think we are going to know within a couple of weeks whether there’s any prospect of a deal between Jeremy Corbyn and Theresa May and whether the Labour Party are going to rescue her premiership. Once it becomes clear that they are not going to rescue her premiership, I don’t really see the point of going on.

“There aren’t Brexit negotiations. It is just that Theresa May and the government don’t want to break off the talks because that would be an admission that they have run out of options.”

The former chancellor’s comments came after Sir Graham said outside a meeting of the 1922 committee on Wednesday he had held two meetings with the prime minister in recent days.

He refused to confirm to journalists whether her departure from Downing Street will be discussed next week, but a second Tory MP declared: “A week has been bought.”

Sir Graham also said it was the government’s intention to bring back the withdrawal agreement bill “sooner rather than later” and “before the European elections”.