Ministers are at risk of a second defeat in the House of Lords over the bill paving the way for Brexit talks.
Peers may back calls for a “meaningful vote” on the final terms of the UK’s withdrawal from the EU and its future relations during a debate on Tuesday.
No 10 has assured Parliament it will get a say on the outcome, but opponents want the option of a veto, even if no Brexit deal is agreed.
Ministers have appealed to peers not to limit Theresa May’s room for manoeuvre.
Peers have already voted in favour of guaranteeing the rights of EU residents to remain, putting them on a collision course with MPs who rejected the idea.
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The prime minister wants to notify the EU by the end of March that the UK is leaving the bloc – triggering Article 50 of the Lisbon Treaty – but needs the approval of Parliament to do so.
The House of Commons has approved legislation which would kick-start the two-year process, but the Lords has already amended the bill and Labour, Lib Dem and crossbench peers are seeking further changes when debate resumes on Tuesday.
MPs voted by a margin of 326 to 293 against giving Parliament a potentially decisive say over the final deal after ministers promised they would be consulted.
But a Labour amendment tabled in the House of Lords, backed by leading crossbench peers, would require the explicit approval of Parliament before Mrs May could conclude any deal on leaving the EU or establishing a new relationship.
The amendment, which has the backing of leading QC Lord Pannick, former diplomat Lord Hannay and Conservative peer Viscount Hailsham, would also give Parliament an effective veto if no deal was struck and Mrs May decided to leave the EU “without an agreement as to the applicable terms”.
Ministers have previously indicated that were MPs or peers to reject a deal agreed with the other 27 states or if no acceptable deal could be reached, the UK would still leave, potentially defaulting to World Trade Organisation rules on commerce.
Critics say this would be highly damaging economically and Parliament must have the authority to send ministers back to the negotiating table to secure new terms.
Should the Lords amend the bill, the matter would pass back to the House of Commons, which would be expected to reject it again – potentially leading to a stand-off between the elected and unelected chambers.
Earlier on Monday, former Chancellor Lord Lamont warned that many of those seeking a meaningful vote actually wanted to stop Brexit in its tracks.
“Amendments should not be used as a cover by those who are seeking to oppose the results of the referendum,” he said in a speech in London.
“I hope my colleagues in the Lords will see sense.”
Meanwhile, the prime minister has been warned not to use her proposed Great Repeal Bill to avoid full parliamentary scrutiny of the Brexit process.
The Great Repeal Bill will scrap the 1972 European Communities Act, which paved the way for the UK to enter the then-EEC, ending the legal authority of EU law.
It will also transpose EU regulations into domestic law, crucially allowing them to be altered or removed after Brexit.
Senior peers on the House of Lords Constitution Committee said Mrs May must not use the legislation to “pick and choose” which elements of European law she wanted to scrap or alter without Parliament’s full involvement.
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