Theresa May is meeting EU officials as the two sides scramble to finalise a Brexit deal in time for Sunday’s summit of European leaders.
The EU is in a race against time to complete the text of its declaration on future relations with the UK, amid concerns from several member states.
Stumbling blocks remain over UK access to the EU single market, access to UK waters for EU boats and Gibraltar.
The PM is under pressure from her own MPs not to give any further ground.
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During a flying visit to Brussels designed to prepare the ground for this weekend’s summit of EU leaders, Mrs May is holding talks with European Commission president Jean-Claude Juncker.
Mr Juncker has cancelled a two-day trip to the Canary Islands, on Thursday and Friday, to deal with “the many important events taking place at the moment”.
European Commission Vice-President Valdis Dombrovskis said “sherpas” – officials tasked with doing the detailed work ahead of summits – were due to meet on Friday to work on the final texts of the withdrawal agreement and the future relationship.
German Chancellor Angela Merkel said: “Both documents need to be ready by Sunday so that we can sign the exit agreement and accept the declaration on the future relationship.”
Asked if the summit could be cancelled, Downing Street said the agenda had been published and it “looked forward to attending”.
Before heading for Brussels, Mrs May came under fire from every Brexit faction in the House of Commons at a noisy Prime Minister’s Questions – from those who want another referendum, to those who want Britain to leave the EU without a deal.
One of her own MPs, Andrew Rosindell, called on the PM to “lead our country in a new direction, completely cutting away the tentacles of the EU over our cherished island nation once and for all”.
Mrs May responded by saying her deal delivered on the promises of Brexit and ensured a continued close trading relationship with the EU.
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Labour leader Jeremy Corbyn zeroed in on comments by new work and pensions secretary Amber Rudd, who said MPs would prevent a no-deal Brexit, apparently putting her at odds with the PM’s “no deal is better than a bad deal” stance.
He asked: “Does the prime minister agree there are no circumstances under which Britain would leave with no-deal?”
Mrs May replied “no” and said the alternative to her deal would “either be more uncertainty, more division or”, in what looks like the emerging new emphasis from her government, “it could risk no Brexit at all”.
Mr Corbyn said that “if the government can’t negotiate an alternative then it should make way for those who can and will”.
Mrs May replied: “He is opposing a deal he hasn’t read, he’s promising a deal he can’t negotiate, he’s telling Leave voters one thing and Remain voters another – whatever (Mr Corbyn) will do, I will act in the national interest.”
Mrs May also rejected a call from the SNP’s Ian Blackford to renegotiate her Brexit deal to keep the UK in the single market and customs union, saying it would “frustrate the vote of the British people”.
And she branded Green MP Caroline Lucas’s call for another referendum, on the grounds that public opinion had shifted since the 2016 referendum, “absolutely ridiculous,” saying the public had given this Parliament “an instruction” to leave the EU.
Amber Rudd earlier said Parliament would not accept a no-deal Brexit.
She told BBC Radio 4’s Today programme: “It’s my view that parliament, the House of Commons, will stop no deal. There isn’t a majority in the House of Commons for that to take place.”
Asked if she would back another referendum, like some of her fellow Remain-voting Tory MPs on the backbenches, Ms Rudd said: “I don’t think we are looking at another referendum.”
She said MPs would “take a careful look over the abyss” and decide it was in the “best interests of the country” to vote for Theresa May’s Brexit withdrawal agreement.
Mrs May appears to have faced down the threat of a challenge to her position from Brexiteer critics of the deal, for the time being at least.
However, Tory MPs unhappy with Mrs May’s handling of Brexit negotiations want much more clarity on the terms of the UK’s future co-operation with the EU if they are to back the final deal – which will be put before European leaders this weekend.
All sides in the Commons have warned of a “blind Brexit” in which the UK signs up to a series of legally-binding commitments in the draft withdrawal agreement, without similar guarantees over future trading arrangements.
The withdrawal deal was agreed in principle by both Mrs May and the EU last week. It includes a £39bn “divorce bill” and the controversial customs “backstop” which keeps the UK temporarily in the EU customs union as a way of preventing the return of manned customs posts at the Irish border.
However, the joint political declaration on future relations – still being drafted – would only set out the shape of the UK’s trading relationship with the remaining 27-nation bloc, without any legal commitments.
Any binding trade deal would still have to be thrashed out in the 21-month transition period after Britain leaves the EU on 29 March 2019.
The BBC’s political editor Laura Kuenssberg said some UK ministers still believed there was time for a few “nips and tucks” to the withdrawal agreement reached in principle last week.
Why is May rushing to Brussels?
By Katya Adler, BBC Europe editor
Could this all be more about optics than nitty-gritty politics?
Grumbling aside, no-one in European circles seriously thinks any EU country will refuse to sign up to the Brexit deal by end of play this weekend.
They’re all keen to avoid a no-deal scenario and they want to help Theresa May get the Brexit texts through a vote in the House of Commons.
Engaging in last-minute political fisticuffs with the EU is arguably advantageous for Mrs May.
A high-drama, climactic Brexit summit ending in a (presumably planned) late night/early morning bleary-eyed but triumphant resolution with EU leaders would allow the prime minister to claim that the final text of the deal was hard fought and hard won… in the fervent hope that will soften the stance of some of her many critics at home.
Discussions in Brussels focus on the political declaration outlining relations from the scheduled end of the transition period in 2021. Currently running to 20 pages, it will sit alongside the withdrawal agreement.
The BBC understands the intention is still to present a completed text to leaders at Sunday’s summit but opinions differ over how easy it would be to solve the outstanding issues.
Spain has warned it will reject the draft Brexit withdrawal deal without a clarification of the text on future talks on the status of Gibraltar.
Spain maintains a claim to the peninsula, ceded to the British crown under the 1713 Treaty of Utrecht and it wants to ensure that future EU talks with the UK do not cover Gibraltar.
Ambassadors from the EU’s 27 remaining countries had been due to be briefed on the final text on Tuesday but the meeting has been re-scheduled for later this week.
Brexit: May holds talks in Brussels amid scramble to finalise deal}