Theresa May has been given a fresh indication of the difficulties she could face if MPs are given a vote over triggering Article 50 in order to start the Brexit process.
Ministers are challenging a High Court ruling that Parliament must be given a say before the formal two-year process can be started by the Government, but if it comes to a Commons vote a number of MPs have indicated they would oppose the measure unless there are major concessions.
Liberal Democrat leader Tim Farron said his party would vote against Article 50 unless there was a guarantee that the final Brexit deal with the European Union is put to a fresh referendum.
He insisted he respected the decision made by voters in favour of leaving the EU but said nobody should have a deal "imposed" upon them.
Although the Lib Dems only have eight MPs they have more than 100 peers in the Lords, which could spell trouble for the Government if judges rule that a full act of Parliament is required before Article 50 can be triggered, as the legislation would have to clear both Houses.
Mr Farron said he believed the Lords would not get a vote either for or against Article 50 but would be able to move amendments.
The Lib Dem leader said: "We have said we will vote against Article 50 if our red line is not met, and it is a single, simple red line which is that we want to respect the will of the people and that means that they must have their say in a referendum on the terms of the deal.
"It is the only logical and it is the only democratic option on the table. There will be a referendum at the end of this process so that nobody would have imposed upon them something they didn't vote for."
He told BBC Radio 4's Today programme: "We believe that what started with democracy last June - which we totally respect - must not now end up with a stitch-up, with a deal being imposed on the British people that absolutely nobody voted for."
MPs from other parties - including a Labour frontbencher - have indicated they would be prepared to oppose Article 50.
Shadow Foreign Office minister Catherine West wrote on Twitter earlier in November that she would respect the wishes of her constituents, who voted to Remain.
"I stand with the people of Hornsey and Wood Green, and I will vote against Brexit in Parliament," she said.
Another Labour MP, Helen Hayes, said she would also be prepared to defy the Labour whip if necessary.
She told Today: "I had somebody in my surgery last week who was in tears because of Brexit and I see genuine distress amongst my constituents about what this path means.
"I would not be representing them if I voted to trigger Article 50 on the basis of no information from the Government about the path that they would then take us on."
The Government will challenge the judges' ruling at the Supreme Court in December, arguing that prerogative powers could be used to trigger Article 50.
An outline of the grounds for appeal published by the Brexit Department said the High Court was mistaken and should have accepted "the Crown retains the power to give effect to the result of the EU referendum" by taking the "first step in the process" by notifying that it is triggering Article 50.
The Government's lawyers will argue that "in any event, the continued existence of the power to take that first step is clearly established and authorised by Parliament".
Brexit Minister David Jones said: "Parliament voted by a margin of six to one to put the decision on whether to remain in, or leave, the EU in the hands of the British people.
"Now, because they didn't like the first answer, Liberal Democrat and Labour MPs seek to put the question all over again in hope of a different answer.
"They are attempting to thwart and reverse the decision that was taken on June 23.
"Only the Conservatives can be trusted to respect the outcome of the referendum and make a success of Brexit."