Chancellor Philip Hammond has hinted Theresa May could remain in office until October – the new deadline for negotiations over Brexit to conclude.

Despite dozens of the prime minister’s own colleagues calling for her resignation in recent weeks, Mr Hammond said Ms May did not have “any intention” of leaving before the first stage of the Brexit process is over.

The Tory leader has previously told MPs that she was “not prepared to delay Brexit any further than 30 June”, and that she would leave Downing Street after a withdrawal agreement had been secured in parliament.

But at an emergency summit this week in Brussels, EU leaders extended the Article 50 negotiating period until 31 October, with the option of the UK leaving the bloc if a deal is agreed beforehand.

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Speaking to Bloomberg, Mr Hammond hinted Ms May could stay on until October: “The prime minister has said that she will leave once she has done the deal and taken us out of the European Union.

The chancellor said that as far as he was aware “she doesn’t have any intention of leaving until that deal is done”, adding: “So, she is a person with a strong sense of duty. She feels that she has got a duty, and an obligation to the British people to deliver Brexit and she will certainly want to make good on that obligation.”

Pressure will also be immense on Ms May to outline her departure timeline ahead of the Conservative Party’s annual conference in Manchester this autumn, with many of those hoping to succeed her wanting to use this opportunity for a change in direction.

Asked about the implications of a leadership contest, the chancellor said: “Let’s be honest, we have already got people jockeying for position to succeed her, but that’s just one of those things.”

If Ms May fails to gain MPs’ support for a Brexit deal in the coming weeks, the UK will be forced to participate in the European elections on 23 May, which Mr Hammond also described as a “pointless exercise”.

“The only way we can avoid that is by getting a deal agreed and done quickly, and if we can do that by 22 May then of course we can avoid fighting European parliamentary elections,” he said.”But in any case we want to ensure any British MEPs that are elected never have to take their seats.”

Mr Hammond’s remarks came as a poll by YouGov for The Times showed the Conservatives losing significant support, and indicated the party could be in for a challenging time at the European elections next month if the UK participates.