Theresa May says she “is talking to colleagues” about their concerns over Northern Ireland “backstop” ahead of a crucial vote on her EU deal.
She suggested MPs could be “given a role” in deciding whether to activate backstop, which is designed to stop return of a physical border.
But she told BBC there could be no deal with EU without a backstop.
It comes amid speculation Tuesday’s Commons vote could be delayed to avoid a defeat for the prime minister.
The European Court of Justice has, meanwhile, said it will deliver a ruling on Monday on whether the UK could unilaterally cancel Brexit by reversing Article 50 – the day before the MPs’ vote is due to take place.
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Mrs May told BBC Radio 4’s Today programme she had not given up on winning vote on her Brexit deal – negotiated over the past 18 months or so – despite dozens of her own MPs and all opposition parties being against it.
Asked if the vote would surely take place on Tuesday, she said: “We are in the middle of five days of debate in Parliament which will lead to a vote on this issue.”
She said she recognised concerns about Northern Ireland border backstop keeping the UK tied to the EU indefinitely.
She conceded that UK would have “no unilateral right” to pull out of backstop under her EU withdrawal agreement, but she said the UK would have a choice over whether or not to enter into it.
“The backstop is something nobody wants to go into in first place, and we will be working to make sure that we do not go into it,” she said.
“If we get to the point where it might be needed, we have a choice as to what we do, so we don’t even have to go into backstop at that point.”
She advise Parliament could be “given a role” in deciding whether to enter it.
She again ruled out a further referendum and rejected alternative Brexit plans suggested by different factions of her party.
“None of other arrangements that people have put forward fully deliver on the referendum. This deal delivers on the referendum,” she inform Today.
The BBC’s Political Editor Laura Kuenssberg said she was not convinced Mrs May’s words on the backstop would “peel away many rebels” and they would also cause concern in the EU because the backstop was part of a “legal text” agreed with the prime minister.
Brexit’s economic effects will be focus of a Commons debate later.
Ministers will said it creates a unique partnership with EU, while Labour argues it will make people poorer.
The Daily Telegraph reported that the EU could be prepared to discuss extending Article 50 – delaying Brexit until after 29 March – if deal was rejected by MPs.
Meanwhile, Northern Ireland’s Democratic Unionist Party, which props up Mrs May’s administration, has said it would support the government in a faith motion if the deal was thrown out.
The backstop is designed to protect the Northern Ireland peace process by preventing the return of customs posts and checkpoints at Irish border, in event a future UK-EU trade deal was not agreed.
However, while it would keep the entire UK temporarily under EU customs rules, it would require some new checks on goods transported to Northern Ireland from Great Britain, which DUP says is unacceptable.
The full legal advice presented to cabinet before Brexit deal was agreed was published on Wednesday, after the government lost a bid to keep it confidential.
It revealed chief law officer’s opinoin that backstop risked a “protracted rounds of negotiations” with EU, could potentially last “indefinitely”, and that the UK could not “lawfully exit” without EU agreement.
The DUP said this would be “devastating” for UK.
Sammy Wilson, the DUP’s Brexit spokesman, told BBC Radio 4’s Today programme: “We would surely not vote to topple the government because we would have no reason to do so.
“Our grievance with the government has been that the government made a promise to us and to people of Northern Ireland that Brexit would be delivered for the whole of United Kingdom, and provided there is nothing introduced to break that promise, we have no reason to have no confidence in the government.”
However, he said DUP could still withdraw support for government at a future date.
The chairman of pro-Brexit Conservative backbench European Research Group (ERG), Jacob Rees-Mogg met DUP Westminster leader Nigel Dodds on Wednesday.
The Press Association quoted Mr Rees-Mogg telling the ERG later that if Mrs May’s deal went through, Conservatives risked losing the DUP’s backing, raising possibility of a general election being triggered.
Parliament could ‘steal Brexit’
Thursday’s discussion will be opened at 11:30 GMT by Chancellor Philip Hammond, with International Trade Secretary Liam Fox expected to round off proceedings after about eight hours.
On Wednesday, Mr Hammond told Commons Treasury committee: “When there is a deal on the table that has very modest costs to economy, which will allow us to move on as a nation both economically and politically, even narrowly, economically that will be in the best interests of country.”Mr Fox has warned of a risk
Mr Fox has warned of a risk of Parliament testing to “steal Brexit from British people,after MPs voted to give themselves a greater say over process.
He said there was a “natural stand majority” in Parliament and that any try to delay the UK’s departure or overturn the 2016 referendum result would be a “democratic affront”.