May has promised to begin the process by the end of March but the court's decision raises the prospect of a protracted parliamentary debate before then, in a chamber that overwhelmingly opposed Brexit and may seek to soften the break with the EU.
The pound – which has tumbled to multi-year lows since June's referendum to leave the EU – soared against the dollar and euro, standing at $1.2474 in Asian trade on Friday, November 4.
EU leaders have been pressing for a swift divorce, and May has arranged a phone call with European Commission chief Jean-Claude Juncker on Friday, a commission spokesman said.
The case challenged the government's right to use "historic prerogative powers" – a type of executive privilege – to trigger Article 50, which begins a two-year countdown to exiting the EU.
"We hold that the secretary of state does not have power under the crown's prerogative to give notice pursuant to Article 50... for the United Kingdom to withdraw from the European Union," the judgement said.
May's office said it was "disappointed" at the decision and would appeal, with the case now expected to be heard in the Supreme Court in early December.
"The country voted to leave the European Union in a referendum approved by act of parliament. And the government is determined to respect the result of the referendum," it said in a statement.
A spokeswoman added: "Our plans remain to invoke Article 50 by the end of March."
Brexit minister David Davis said the government would fight the ruling, insisting that result of the referendum must be respected.
"That's why we're appealing it and we're appealing it intending to win that appeal," he said in a television interview.
'Betrayal may be near'
Robert Pigney, one of the claimants in the case, told Agence France-Presse that the ruling was "an immense victory for the British people".
"It's very important that our elected representatives in parliament remain in control of our future," he said.
Nigel Farage, the interim leader of the UK Independence Party who led the Brexit campaign, warned there would be public outrage if parliament went against the referendum result.
"I worry that a betrayal may be near at hand," he said.
"I now fear that every attempt will be made to block or delay the triggering of Article 50. If this is so, they have no idea of the level of public anger they will provoke."
Fellow Brexit campaigner and former Conservative minister Iain Duncan Smith accused the judges of triggering "a constitutional crisis".
"It's literally pitting parliament against the will of the British people," he told Sky News.
Trevor Tayleur of The University of Law added it was "hard to think of a judgement that has had such a dramatic impact on government policy concerning such a crucial constitutional and political issue."
'Transparency and accountability'
Most members of the House of Commons wanted to stay in the EU, but commentators believe there is no majority support for reversing the referendum result, which was backed by 52% of British voters.
Opposition Labour leader Jeremy Corbyn, whose party opposed Brexit, said he respected the decision of the British people.
"But there must be transparency and accountability to parliament on the terms of Brexit," he said.
"Labour will be pressing the case for a Brexit that works for Britain, putting jobs, living standards and the economy first."
May has so far declined to outline her negotiating strategy, insisting that showing her hand would damage her chances of achieving the best outcome.
But she has indicated she will prioritize cutting immigration, a move that EU leaders have warned is incompatible with staying part of the European single market. – Rappler.com