Jeremy Corbyn has insisted Labour will not block Article 50 despite the prospect of a revolt by his MPs and peers.
The Labour leader insisted the referendum result must be respected, with MPs being asked to support it "however difficult they might find that".
Theresa May could be forced to seek parliamentary approval for the formal step needed to start the Brexit process if the government loses its Supreme Court appeal next week.
Mr Corbyn has said Labour MPs will be asked to vote in favour of triggering Article 50, although he has not specified whether that would mean a full three-line whip compelling them to do so.
Prominent Labour parliamentarians including former cabinet minister Lord Hain and ex-chairman of the Commons Foreign Affairs Committee Mike Gapes have vowed to rebel if Mr Corbyn does impose a whip on any vote.
Dozens of MPs could rebel on the matter, with reports suggesting the figure could be as high as 80.
"We've made it clear that the referendum result must be respected, it was a UK wide referendum, it delivered a result," Corbyn said in Glasgow.
"It didn't deliver a recommendation that there should be massive job cuts and impoverishment across the UK, it simply said we would be leaving the European Union.
"And I have made very clear that we will do two things - we won't block Article 50 because we have to respect the result of the referendum.
"But we will also use the opportunity of the initial Bill to implement Article 50 and the Great Repeal Act, or whatever they are going to call it, when it comes out in May, to put forward a case for accessing European markets, for social justice across Britain and for greater democracy across our whole society.
"And Labour MPs are being asked to respect the result of the referendum, however difficult they might find that."
Lord Hain told the Press Association that he was reflecting the views of the majority of Labour voters and warned that Brexit would be "disastrous for the country".
For me it's a matter of conscience. I just think this is a disastrous decision for Britain and, particularly, for those least able to defend themselves," Hain said.
"I would have thought it would be sensible for all Labour MPs and Labour peers to be able to vote according to their consciences on this one."
