A government source said the talks – which have been ongoing since early April – needed to be brought to a conclusion one way or another by the middle of next week.
Labour insiders insisted they knew nothing about the deadline set by Downing Street.
Senior frontbenchers from both camps met for the latest round of talks on Monday, and a spokesman for the Prime Minister said they had been “serious and constructive”.
“Further talks will now be scheduled in order to bring the process toward a conclusion,” he said.
But the Whitehall source insisted that the negotiations could not go on indefinitely because the British public want the see Brexit delivered as soon as possible.
Labour has been using the talks to press its case for ministers to back a customs union with the European Union – a move that would anger many of Mrs May’s MPs who believe it would hinder Britain’s ability to strike post-Brexit trade deals.
Speaking after the weekly meeting of Mrs May’s top team, the PM’s spokesman said: “Cabinet discussed the need to secure safe passage of the Withdrawal Agreement Bill as soon as possible in order to deliver on the result of the referendum. There’s an understanding on the need to make progress on delivering Brexit the way to leave the European Union with a deal is by securing safe passage of the WAB.”
He added: “I would point you to the need to make progress as soon as possible.”
Foreign Secretary Jeremy Hunt has meanwhile described weeks of discussions between the two sides have been “more detailed and productive than we thought and expected”.
But he warned that some Conservative MPs could be forced to drop their support for the Prime Minister’s Brexit deal if she gives too much ground to Labour.
He told The Telegraph: “There is always a danger of doing a deal with Labour that [means] you lose more Conservative MPs than you gain Labour MPs, but I think the essential question is whether Labour are serious about delivering Brexit.”
