Philosopher AC Grayling, who campaigned for the UK to stay in the EU, says the court's verdict is a "vindication of the view that Parliament is the arbiter of what happens in and to our country".

He thinks the referendum was "advisory and non-binding" and - unlike most MPs - thinks Parliament "has an opportunity to save the UK from a disastrous course of action".

Victoria Derbyshire

Former Conservative leader Iain Duncan Smith winds up his remarks by saying while he is "all for debate", it would be "unacceptable if the Lords decide to block" Article 50 because Brexit had been decided by "the will of the British people".

He warned Lib Dem peers, whose numbers he says are disproportionate with the size of their presence in the Commons, "not to thwart the will of the Commons and ultimately of the British people".

Lib Dem peer Baroness Kramer stressed that her party will "try to use that power to amend" the bill.

Former Conservative chancellor Ken Clarke insisted: "No one is going to block leaving - the question is in the end government has to get Parliament's approval for the policies its pursuing."

Dominic Casciani
Home Affairs Correspondent

During the four-day hearing in December, the justices heard arguments that Northern Ireland had a unique place in the UK constitution because of the nature of the 1998 Belfast Agreement and the devolved bodies that flowed from it. 

Counsel argued that Northern Ireland’s constitution cannot be changed without a vote by its people. In its judgement, the Supreme Court unanimously ruled that not only did the devolved bodies have no role in deciding the future of the UK as a whole in the EU, Northern Ireland had no special status beyond this either. They ruled (paragraphs 126 – 135) that while Northern Ireland’s people did indeed have a fundamental constitutional say on being part of the UK, that did not extend to being part of the EU. 

The court said:

Welsh Assembly members do not have to be legally consulted on the article 50 Brexit process, the Supreme Court rules.

UKIP leader Paul Nuttall warned MPs and peers not to hamper the passage of the Article 50 legislation.

He said: 

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Ken Clarke, former Conservative chancellor and Remain campaigner, said he did not understand why the government "has been bothering to resist" a vote on Article 50.

He said he hopes that if the "government eliminates discussion" on the new bill, Parliament "will start to hold the government to account".

But former Conservative leader Iain Duncan Smith, a prominent Leave campaigner, said "there's going to be a vast amount of debate in both Houses of Parliament" about the repeal of the European Communities Act, which means "the public will be sick and tired" of it.

Nick Eardley
BBC Scotland Westminster correspondent

Brexit now returns to the political realm - and the fundamental political arguments remain the same.

The SNP will try to amend the legislation to give the Scottish government a say through the joint ministerial council. The UK government will continue to argue it is seeking to carry out the will of the UK electorate and that this is a UK-wide issue.

And the divisions the referendum result threw up are likely to resurface in the Commons.

It's feasible that, if no amendments are accepted, 58 of Scotland's 59 MPs could vote against triggering Article 50.

Today's decision doesn't stop Brexit. It might not even delay triggering Article 50. But it means the focus returns to politics.

BBC Monitoring
News from around the globe

The German papers have the ruling as their top story online, with Frankfurter Allgemeine Zeitung, external saying it "could have been worse" for Theresa May.

Sueddeutsche Zeitung, external and news magazine Der Spiegel, external wonder whether the ruling could disrupt Mrs May’s timetable for triggering Brexit.

But a commentary , externalin Frankfurter Allgemeine Zeitung – written ahead of the announcement - cautions that, whatever the Supreme Court says, “Britain will leave the EU”.

Die Welt, external is not so sure. It quotes the head of the German Institute for Economic Research, Michael Huether, as saying that Britons will realise that Brexit is economically unaffordable, and that there is a one-in-three chance of Parliament stopping Brexit altogether at some point down the line.

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Shadow Brexit secretary Keir Starmer says he hopes the Supreme Court ruling will mean MPs having a vote at a point "at which we can still influence the outcome" of the Brexit negotiations.

He told the BBC he was concerned Theresa May will say: "Here's a deal - take it, or leave it."

"I hope the government will seek the best deal for Britain and be able to bring it back in the national interest," he said.

Sir Keir said his party, Labour, accepted and respected the outcome of the EU referendum "and that means we will not seek to frustrate the process".

However, he said he accepted "this is a difficult set of decisions for many colleagues who feel very strongly about these issues", adding that the party is handling the situation "collegiately".

Lead plaintiff Gina Miller welcomes the Supreme Court's Brexit ruling - that Parliament must vote on Article 50.

Steven Agnew, the leader of the Green Party in Northern Ireland, says he is pleased the Supreme Court has decided Parliament will have its say on the triggering of Article 50.

He said:

Following the Supreme Court ruling, a spokesman for Number 10 said:

The Scottish National Party has welcomed the Supreme Court ruling, but vowed to put forward 50 "serious and substantive" amendments to UK government legislation.

Former leader Alex Salmond said:

• THE 1972 Act that took the UK into the then EEC creates a process by which EU law becomes a source of UK law. 
• So long as that act remains in force, it means that EU law is an “independent and overriding source” of our legal system. 
• Unless Parliament decides otherwise, this remains the case 
• Withdrawal from the EU makes a fundamental change to the UK’s constitutional arrangements because it will cut off the source of EU law. 
• Such a fundamental change will be the inevitable effect of a Notice being served
• The UK constitution requires such changes can only be made by Parliament 
• The fact that withdrawal from the EU would remove some existing domestic rights of UK residents also renders it impermissible for the Government to withdraw from the EU Treaties without prior Parliamentary authority.

Brexit Secretary David Davis is set to give a House of Commons statement on the Supreme Court judgement at 1230 GMT, according to the Speaker's Office.

Shadow Brexit secretary Keir Starmer will be speaking for Labour.

Lord Neuberger says Parliament must vote on whether the government can start Brexit.

Labour leader Jeremy Corbyn says his party will not "frustrate" the process for invoking Article 50.

But he said his party would seek to amend the legislation the government has been forced to produce in order to prevent Theresa May allowing the UK to become a "bargain basement tax haven".

He said: