Labour and the Scottish National Party have promised to make amendments to the Government's bill on Article 50, following today's Supreme Court verdict.
The Lib Dems have made an even stronger statement, suggesting that they will not vote for the legislation unless there is a categorical promise that the British people get to vote on the final Brexit deal.
The Supreme Court this morning ruled that Theresa May cannot trigger Article 50, and thus begin the Brexit negotiations, without consulting lawmakers. However, the court has also ruled that the Scottish Parliament, Northern Ireland and Welsh assemblies are not entitled to a say.
A spokesperson for Labour leader Jeremy Corbyn has said: “Labour respects the result of the referendum and the will of the British people and will not frustrate the process for invoking Article 50.
“However, Labour will seek to amend the Article 50 Bill to prevent the Conservatives using Brexit to turn Britain into a bargain basement tax haven off the coast of Europe."
The party wants to build in "principles of full, tariff-free access to the single market," and ensure workers' rights, social and environmental protections are in place.
The spokesperson added: “Labour is demanding a plan from the Government to ensure it is accountable to Parliament throughout the negotiations and a meaningful vote to ensure the final deal is given Parliamentary approval.”
The SNP, which has used Brexit as the basis for a fresh Scottish independence campaign, has pledged table 50 "serious and substantive" amendments.
Nicola Sturgeon's party is calling on the government to publish a white paper, and is also demanding that Britain's devolved regional assemblies are consulted - in defiance of the Supreme Court's ruling.
Tim Farron, the leader of the LIberal Democrats and the most openly anti-Brexit of all Britain's political leaders, has said that he welcomes the judgement given today, however has criticised the Conservatives.
He said: “This Tory Brexit government are keen to laud the democratic process when it suits them, but will not give the people a voice over the final deal. They seem happy to start with democracy and end in a stitch up.
“The Liberal Democrats are clear, we demand a vote of the people on the final deal and without that we will not vote for Article 50.”