EU leaders have “lost patience” with Britain and do not want to grant another Brexit extension when time runs out in October, Ireland’s prime minister has said.

Arriving at a meeting with his 27 counterparts, where leaders will check in on the Brexit process, Leo Varadkar said there was “enormous hostility” to another delay in EU capitals.

He said his feeling was that an extension would be granted only to allow for a general election or second referendum.

The current extension secured by Theresa May is set to expire on 31 October, when the UK will crash out with no deal if it does not ratify the withdrawal agreement or decide to remain instead.

“There’s very much a strong view across the European Union that there shouldn’t be any more extensions. While I have endless patience, some of my colleagues, quite frankly, have lost patience with the UK – and there’s enormous hostility to any further extension,” Mr Varadkar told reporters on the doorstep of the meeting.

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“So I think an extension could really only happen if it were to facilitate something like a general election in the UK, or even something like a second referendum, if they decided to have one. What won’t be entertained is an extension for further negotiations or further indicative votes. The time for that has long since passed.”

Other EU leaders arriving at the same meeting also took the opportunity to warn that the withdrawal agreement struck by Theresa May would not be renegotiated.

Asked about the ongoing Tory leadership race, Luxembourg’s prime minister Xavier Bettel said: “It’s the choice of the Tories, it’s not my choice. Brexit was neither my choice. If they choose Boris Johnson, he will have to deal with us on the agreement we have done with Theresa May.”

Arturs Krisjanis, Latvia’s prime minister, laughed when asked whether he could work with Boris Johnson. He replied: “Every country has their internal processes, how they choose their leaders. Great Britain has going through one of these processes. I’m very much looking forward to continuing good cooperation with Great Britain.”

The Dutch prime minister, Mark Rutte, was scathing when asked about the leadership candidates’ Brexit positions, telling reporters: “During the election campaign for the new leadership of the Tory party it seems their positions have shifted so much so it is difficult for me to assess exactly.” He added: “I’m not going to comment on the leadership candidates.”

The 28 EU leaders will briefly discuss Brexit on Friday, the second day of the summit. Britain’s departure is taking a back seat for once at this meeting, with the main focus being filling the EU’s top jobs and a debate over bloc-wide climate change policy.

Arriving at the summit – which is her last scheduled as prime minister – Theresa May told reporters: “We will be looking for the UK to do what we have always said we would do, which is to make a constructive contribution as we remain a member of the European Union [and] for that period of time we will continue to meet our rights and obligations.

“But of course we will be leaving the EU and we look forward to developing a close partnership with the EU when we’ve left.”

But the prime minister twice sidestepped questions about whether she would miss attending the Brussels gatherings.