Theresa May is to update MPs on her Brexit progress on Tuesday, a day earlier than previously announced, No 10 has said, while stressing the prime minister had completely ruled out Jeremy Corbyn’s proposal of a departure deal involving customs union membership.

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“We are absolutely clear on this: we’re not considering Jeremy Corbyn’s customs proposals; we’re not considering any proposals to remain in the customs union. We must have our own, independent trade policy,” May’s spokesman said.

On Sunday, May responded to Corbyn’s letter, from last week, that set out Labour’s conditions for backing any Brexit deal, one of which was membership of a permanent customs union.

While the prime minister made it plain she did not want this, several newspapers on Monday said May had held open the door to the issue, and thus the idea of a softer Brexit.

Speaking earlier on Monday, the prisons minister, Rory Stewart, insisted May opposed Labour’s customs union idea, but said there was nonetheless “a lot of common ground” between the parties.

May’s spokesman set out the timetable for the latest Brexit updates. The prime minister will make a Commons statement on Tuesday, before MPs debate an amendable motion on Thursday, allowing them to try and shape the process.

The statement had been expected for Wednesday, but the spokesman said it had been moved forward to give MPs an extra day to draft amendments.

There would definitely not be a meaningful vote on a revised deal this week, the spokesman added, with May committed only to putting it to MPs “as soon as possible”.

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Asked if May was looking at some sort of compromise with the opposition leader, Stewart told BBC Breakfast: “Yes. I think she feels, as I do, that there isn’t actually as much dividing us from the Labour party as some people suggest.”

Speaking on BBC Radio 4’s Today programme, Boris Johnson, a leading Brexiter, said May should focus on renegotiating the Irish backstop issue rather than join Corbyn in what he called “a complete U-turn”.

“He now wants to frustrate Brexit very largely by staying in a permanent customs union,” the former foreign secretary said.

Other elements of May’s letter indicated she was hopeful of at least winning over some wavering Labour MPs when her plan is next voted on in the Commons, which is unlikely to be before the end of the month or later.

In her response to Corbyn, May made a concession on environmental and workers’ rights, discounting his idea of automatic alignment with EU standards but suggesting instead a Commons vote every time these change.

Stewart said: “What she is saying is that we have a lot of common ground, a lot more common ground perhaps than people have acknowledged, on things like environmental protections, workers’ rights, making sure that we get investment into areas of the country which haven’t done as well out of the last few years as other parts of the country.”

If May had hinted she could accept a customs union it would have risked splitting her party. Liz Truss, the chief secretary to the Treasury, indicated she would resign if this happened. She told Sky’s Sophy Ridge on Sunday: “I absolutely do not think that should be our policy.”

May’s letter came amid a growing presumption that while she remained officially committed to putting a revised Brexit plan to MPs as soon as possible, in practice this was unlikely to happen before the end of February, if not later.

The communities secretary, James Brokenshire, said on Sunday that if no finalised deal were put to the Commons by 27 February, MPs would again be given another amendable motion to consider, allowing them to block a no-deal departure or make other interventions.

Later on Monday, the Brexit secretary, Stephen Barclay, will go to Brussels to meet the EU’s chief negotiator, Michel Barnier, after the PM’s meetings in Brussels last week.

In her letter to Corbyn, May argued that her own Brexit plan “explicitly provides for the benefits of a customs union” in terms of avoiding tariffs, while allowing “development of the UK’s independent trade policy beyond our economic partnership with the EU”.

She wrote: “I am not clear why you believe it would be preferable to seek a say in future EU trade deals rather than the ability to strike our own deals?”

With the deadline fast approaching, business leaders have called for swifter action. The head of the CBI, Carolyn Fairbairn, said the UK was “in the emergency zone of Brexit now” and the confusion would not only affect jobs and investment, but harm the UK as a long-term business destination.