No 10 has indicated that progress has been made in the Brexit talks over the last 24 hours, although there is not yet a final text ready to be put in front of senior ministers for approval.

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The prime minister’s official spokesman told reporters at a morning briefing that “there are a small number of outstanding issues as the UK pushes for the best text that can be negotiated”.

Cabinet members were briefed on the status of the talks by Theresa May earlier in the morning, at their regular weekly meeting on Tuesday, and remain on standby to sign off any withdrawal agreement struck with Brussels in a special session.

Ministers had a 45-minute discussion about Brexit, with Theresa May giving an update on the status of the negotiations and Dominic Raab, the Brexit secretary, going over no-deal preparations. No 10 said the discussion was “constructive”.

British and EU negotiators are expected to work through the day and into the evening in an attempt to strike an agreement that could be put to the cabinet on Wednesday and hit the deadline to hold a November European summit.

However, No 10 sources cautioned that it was not yet certain the deadline would be met. If an agreement cannot be reach in principle by the end of Wednesday, it will not be possible to sign off the Brexit deal at EU level until a summit most likely on 13-14 December.

Earlier the Cabinet Office minister, David Lidington, said a deal could still be reached within the next 48 hours in time to trigger an emergency November summit, but said progress was “not at all definite”.

The prime minister’s de-facto deputy said negotiators had worked late into the night and an agreement was “almost within touching distance”, but there was still disagreement over the key point of contention – an exit mechanism for the Irish backstop proposal.

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Cabinet Brexiters have insisted the UK must have the power to unilaterally leave the “temporary” customs arrangement that has been negotiated as a means of avoiding a hard border in Ireland.

Lidington said the backstop agreement was one of the “outstanding issues that is being negotiated in the endgame” and it “clearly has to be something that is temporary and not indefinite”.

He said there could be an agreement within the next two days, but negotiators were still a distance apart. “Still possible but not at all definite, I think pretty much sums it up,” he told BBC Radio 4’s Today programme.

“We are not quite there yet. This was always going to be an extremely difficult, extremely complex negotiation, but we are almost within touching distance now. But, as the PM has said, it can’t be a deal at any price. It has got to be one that works in terms of feeling we can deliver on the referendum result, and that is why there is a measure of caution.”