A group of MPs from the Liberal Democrats, Labour and SDLP have said they will vote against the triggering of Article 50.
Judges at the High Court ruled Parliament would have a say in when and how the process is initiated and some MPs have indicated they will vote against the bill.
Tim Farron, the leader of the Liberal Democrats, said his party would oppose Article 50 being triggered if there wasn’t a second referendum on the terms of the UK’s Brexit deal.
"It is the only logical and 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 did not vote for,” Mr Farron told BBC Radio 4's Today programme.
“The clearest example, just over a week ago, is of Stephen Phillips, a Conservative MP who resigned from parliament having voted leave and being a very active leave campaigner, who said, 'Hang about, I didn’t vote to leave the single market'".
He also described the potential deal as being a “stitch-up” that no one voted for.
“We believe what started with democracy in June must not now end up as a stitch-up deal being imposed on the British people that absolutely no one voted for,” Mr Farron added.
Labour has pledged not to vote against the Government’s bill to invoke Article 50 but some MPs have indicated they will rebel, according to the BBC.
Former Labour leadership contender Owen Smith, former minister David Lammy and shadow transport minister Daniel Zeichner have all said they would defy the Labour whip.
The majority of Labour MPs are expected to either support the bill or abstain from voting - leaving it well placed to pass through the Commons.
Labour’s leader in the House of Lords, Baroness Smith, also said peers “will not block” Brexit and will instead “scrutinise” and “examine” the proposal.
“We have to be adult about this. We can’t have the most enthusiastic Brexiteers crying foul every time Parliament asks for more details or seeks to scrutinise,” she said.
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."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies