Europe: Brexit: Ministers vow to fight Article 50 court ruling.
Brexit challenger Gina Miller: "This result is about all our futures"
The government has said it will fight a High Court ruling that could frustrate its timetable for Brexit, claiming that voters want them to "get on with it".
Three judges ruled that Parliament, not the government alone, can trigger the formal process of leaving the EU.
Brexit Secretary David Davis said 17.4 million Leave voters had given the government "the biggest mandate in history" to leave the EU.
The Supreme Court is expected to hear the government's appeal next month.
In the landmark ruling, the High Court judges said the government could not trigger the Article 50 process of formally leaving the European Union alone - they must have the approval of Parliament.
This ruling as a "massive obstacle" for Prime Minister Theresa May, who says she wants to trigger Article 50 by the end of March.
If the government loses in the Supreme Court, it will have to publish some form of new law for MPs - and the House of Lords - to vote on. MPs could then push to set the terms for negotiating withdrawal.
The prime minister's spokeswoman said she would be calling President of the EU Commission, Jean-Claude Juncker, to say she intended to stick to her March 2017 deadline for triggering Article 50.
Amid suggestions of a possible early general election, the spokeswoman added that Mrs May believed "there shouldn't be an election until 2020 and that remains her view".
Mr Davis told the BBC the result of the EU referendum "must be respected".
"Parliament voted by six to one to give the decision to the people, no ifs or buts, and that's why we are appealing this to get on with delivering the best deal for Britain.
"That's the best deal for growth, the best deal for investment, the best deal for jobs. The people want us to get on with it and that's what we intend to do."
But Gina Miller, the lead claimant in bringing the case to the High Court, urged the government to "do the responsible sober thing, which is to do the job we pay them for, to debate all the aspects to do with leaving and then have a vote".
'Legal hammer blow'
She rejected criticism that the case was subverting democracy and said it was "not about politics, this was about process".
"One of the big arguments [in the referendum[ was parliamentary sovereignty... so you can't on the day you get back sovereignty decide you're going to sidestep or throw it away."
BBC legal affairs correspondent Clive Coleman described the ruling as a "legal hammer blow" by the judges, in an important constitutional case that defined the limits of government power.
Analysis
By Eleanor Garnier, BBC political correspondent
It is one of the most important constitutional court cases in generations. And the result creates a nightmare scenario for the government.
Theresa May had said she wanted to start Brexit talks before the end of March next year but this ruling has thrown the prime minister's timetable up in the air.
Campaigners who brought the case insist it was about "process not politics", but behind the doors of No 10 there will now be serious head-scratching about what the government's next steps should be.
This decision has huge implications, not just on the timing of Brexit but on the terms of Brexit. That's because it's given the initiative to those on the Remain side in the House of Commons who, it's now likely, will argue Article 50 can only be triggered when Parliament is ready and that could mean when they're happy with the terms of any future deal.
Of course, it will be immensely difficult to satisfy and get agreement from all those MPs who voted to remain. Could an early general election be on the cards after all?
The government had argued it could use ancient prerogative powers to give effect "to the will of the people".
But the three judges looking at the case found there was no constitutional convention of the royal prerogative - powers used by ministers - being used in legislation relating to the EU.
They added that triggering Article 50 would fundamentally change UK people's rights - and that the government cannot change or do away with rights under UK law unless Parliament gives it authority to do so.
Calling the case "a pure question of law", Lord Chief Justice, Lord Thomas said: "The court is not concerned with and does not express any view about the merits of leaving the European Union: that is a political issue."
What the ruling says
It is a fundamental principle of the UK constitution that Kings' or Queens' powers cannot be used by the government via the Royal Prerogative to change or do away with rights under British law unless Parliament gives it authority to do so. The court looked at examples ranging from the 1600s to the 1970s Laker Airways legal battle
Parliament had a vote on the UK joining the European Union back in the 1970s, so there is no convention of the Royal Prerogative being used in legislation relating to the European Union
Allowing MPs a vote on the final Brexit deal at the end of the negotiations would not amount to parliamentary approval because once Article 50 is triggered there is no way that the UK will not leave the EU, and in doing so existing laws will be changed
David Davis points out that MPs voted by six to one for the referendum to be held, but the judgement says that the referendum bill, and background briefings, made clear that the referendum was advisory rather than mandatory. So even though MPs voted for the referendum, the way it was worded did not hand over the authority to trigger Article 50, in its view
But UKIP leader Nigel Farage said he feared a "betrayal" of the 51.9% of voters who had backed leaving the EU in June's referendum.
"We are heading for a half-Brexit," he said.
"I worry that a betrayal may be near at hand... I now fear that every attempt will be made to block or delay the triggering of Article 50."
Labour leader Jeremy Corbyn said: "This ruling underlines the need for the government to bring its negotiating terms to Parliament without delay. Labour respects the decision of the British people to leave the European Union. But there must be transparency and accountability to Parliament on the terms of Brexit."
Liberal Democrat leader Tim Farron told the BBC: "What the government was seeking to do was to impose a deal that absolutely nobody voted for, that most people who voted to leave wouldn't be happy with and most people who voted to remain wouldn't be happy with, without any kind of Parliamentary scrutiny.
"So it's a terrible shame it had to go to the courts, but what has happened is that democracy and sovereignty have been restored."
The UK voted by 52% to 48% to leave the European Union in a referendum on 23 June.
The EU's other 27 member states have said negotiations about the terms of the UK's exit - due to last two years - cannot begin until Article 50 has been invoked.
Pablo JG Marin- he Mariana DAngelo Editorial Group