Theresa May said ‘I think I’d better leave now’ to other EU leaders, to break an embarrassing silence when they refused to discuss Brexit in front of her.

A witness said the Prime Minister made the remark after trying to push for a quick agreement on the future rights of British citizens in the EU, and vice-versa, at the Brussels summit.

It led to an awkward impasse, because the rest of the EU has demanded the right to exclude Britain when they discuss their side of the Brexit negotiations.

They have also insisted there will be “no negotiations without notification” – meaning they must await the triggering of the Article 50 exit clause, at the start of next year.

“It was a difficult moment for diplomatic etiquette,” one leader’s aide told The Times newspaper.

“‘I think I’d better leave now,’ she said. She was very polite, but it was a bit embarrassing,” he added.

The episode came after footage, when Ms May arrived in Brussels, showed her standing isolated and alone while other leaders greeted each other warmly.

The other 27 leaders were due to hold an “informal” discussion without Ms May, to discuss their approach to the Brexit talks – with, she said, her blessing.

Theresa May refuses to comment on suggestions Brexit deal will take 10 years

In the end, after talks on migration and Syria overran by more than three hours, Ms May did give a Brexit update and appealed for a quick decision on expat rights.

Enda Kenny, the Irish prime minister, said: “She would like to have the question of UK citizens living in Europe and European citizens living in the UK dealt with in the early part of discussions that take place.

Mr Kenny then added: “There was no response.”

The EU’s refusal to discuss the issue until after Article 50 has been invoked has prompted growing calls for Britain to guarantee EU citizens’ right unilaterally.

But Ms May has refused to act, insisting to do so might give less leverage over the future rights of the one million British expats.

At the late night meeting – after the Prime Minister left for her RAF plane back to Britain - the EU leaders spent just 20 minutes discussing Brexit.

They devoted far more time to the consequences of Dutch voters rejecting a landmark association agreement with Ukraine, in a recent referendum.

Other pressing issues included the refugee crisis and ceasefire violations in Eastern Ukraine, talks that dragged on late into the night.