But what about the rest of the political world?
Read More: Live: Government loses Article 50 appeal
Labour leader Jeremy Corbyn said that his party will not "frustrate" moves to invoke Article 50.
However, he added that his frontbench will seek to amend any legislation brought forward by the government.
“Labour will seek to build in the principles of full, tariff-free access to the single market and maintenance of workers' rights and social and environmental protections," he said.
“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 Scottish National Party has also vowed to put forward its own plans to amend any Article 50 bill presented by the government.
In fact, the SNP say they will present 50 “serious and substantive” amendments to legislation.
These will include a call for a government white paper before Article 50 can be triggered, and a demand for Theresa May to gain the unanimous support of the Joint Ministerial Committee, which features the leaders of the devolved administrations.
The latter point comes despite Supreme Court judges ruling the Prime Minister is not required to gain the approval of the Scottish, Welsh and Northern Irish assemblies.
Alex Salmond, the SNP's international affairs spokesman, said: “If Theresa May is intent on being true to her word that Scotland and the other devolved administrations are equal partners in this process, then now is the time to show it.
"Now is the time to sit with the Joint Ministerial Committee and not just casually acknowledge, but constructively engage. Consultation must mean consultation."
The Liberal Democrats
The Europhile Lib Dems have welcomed the fact the decision will allow MPs to vote on Brexit.
"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," Lib Dem leader Tim Farron said.
"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."
Ukip leader Paul Nuttall said the verdict could "embolden" attempts to frustrate last summer's referendum verdict.
"It may give heart to those in the EU, used as they are to ignoring their own people, to attempt to play hard ball in the negotiations," Nuttall said.
"But in the end I am convinced that though this skirmish has been lost in the courts, the war will be won".
Change Britain, formerly the Vote Leave campaign, said the Supreme Court judges had "usefully" made clear the government must issue a short Article 50 Bill.
But Tory MP and Chance Britain supporter Dominic Raab added: "Let's have an end to the wrecking tactics.
"Every democrat in Parliament should now support this legislation, so we can get on and deliver on the will of the British people, and secure the best possible deal for the whole country."
Open Britain, formerly the Britain Stronger In Europe campaign, welcomed the verdict, but said parliament still needed to be given the opportunity to shape the results of the UK's negotiation with Europe.
“Parliament’s legitimate role is not just about the triggering of Article 50 – it is also about the content of the deal the government is trying to achieve," said Labour MP and Open Britain supporter Pat McFadden.
"The Prime Minister set out her objectives last week and parliament has a critical role in scrutinising and debating the effect of her aims on the lives of our constituents, on their rights and freedoms and on their prosperity and opportunities.”