Theresa May is heading for a rebellion over her Brexit strategy after the high court ruled that the UK could not leave the European union without the permission of the British parliament.

Three senior judges ruled on Thursday that the government could not press ahead with triggering article 50 of the Lisbon treaty, the formal process for beginning Brexit, without first consulting MPs and peers in the Commons and Lords.

The decision, made after a legal challenge brought following the EU referendum result in June, is a dramatic setback for the prime minister, who had argued that she had the personal authority to begin the process without a parliamentary vote on the issue.

Downing Street has said they will challenge the judgment and an appeal with the supreme court is expected to be lodged. But David Davis, the Brexit secretary, acknowledged that the ruling (pdf) as it stood meant the UK’s departure from the bloc would require the consent of both MPs and peers through an act of parliament. “The judges have laid out what we can’t do, and not exactly what we can do, but we’re presuming that it requires an act of parliament and therefore both Commons and Lords,” he said.

Parliamentarians are unlikely to block Brexit outright, given that 52% of voters among the public opted, on 23 June, to leave the EU, but the need for legislation gives MPs the opportunity to disrupt the process by demanding May reveals more details about her plan for negotiating the terms of departure.

The Guardian understands that a cross-party group of Tory and Labour MPs met this Thursday afternoon to discuss how the ruling could be used to force May to reveal more about her broad negotiating aims.

The shadow Brexit secretary, Keir Starmer, says the PM must clarify her aims on the single market. Photograph: Ken McKay/ITV/Rex/Shutterstock

Keir Starmer, the shadow Brexit secretary, said he now believed it was “inevitable the prime minister will have to answer the big questions” on whether she wanted the UK to be in the single market or the customs union, as there appeared to be a majority of MPs demanding greater transparency.

“This is about accountability and scrutiny,” he said. “Very many MPs accept and respect the referendum of course, but the terms upon which we exit are vitally important. I think there is now consensus that the prime minister has got to disclose the overarching strategy. The idea that we are all to be kept in the dark until some time in 2019 only has to be said to be rejected.”

May has repeatedly insisted that she will deliver the “best possible deal for the country” but has so far refused to specify whether that deal would include access to the single market or enhanced immigration controls.

Within hours of the judgment senior Conservatives were openly calling for a change of approach. Andrew Tyrie, chair of the Treasury committee, said May’s government needed to be “much more transparent about its objectives in the negotiations, in some detail, and the sooner the better”.

He added: “It should also ensure that parliament can scrutinise the objectives and vote on them. The UK is leaving; a public debate is needed about where we want to arrive. Before taking off, it is always a good idea for the pilot to discuss with the passengers and crew where they might want to land.”

Nicky Morgan, the former education secretary, told BBC Two’s Victoria Derbyshire show: “It does need to be not just a vote, but a formal short bill about the triggering of article 50, and then the focus is on that. The other thing, of course, that parliament will want then is a clearer plan on the government’s Brexit plans and that will be, I think, important in helping the government to win that vote.”

On the other side of the debate the ruling infuriated many eurosceptics, with several Tory MPs suggesting May should call an early general election to get another mandate from voters.

Dominic Raab, the former minister and Tory MP, said any attempt to stall the triggering of Brexit could increase the chances of an early general election. “If we get to the stage where effectively [some MPs] are not willing to allow this negotiation to even begin, I think there must be an increased chance that we must go to the country again. I think that would be a mistake and I don’t think those trying to break the verdict of the referendum would be rewarded,” he said.

Former UKip leader Nigel Farage warned on Thursday of ‘public anger’ over a Brexit delay. Photograph: Frederick Florin/AFP/Getty

Douglas Carswell, the Ukip MP, even suggested it showed there needed to be reform of judicial appointments, while the party’s interim leader, Nigel Farage, said he feared 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.”

The prime minister is expected on Friday to speak to Jean-Claude Juncker, the European commission president, to discuss her plans for keeping the article 50 process on track.

However, the unanimous judgment delivered by three of the most senior judges in England and Wales will make it difficult for government lawyers to overturn the ruling in the supreme court and avoid delay.

The three judges, the lord chief justice, Lord Thomas, the master of the rolls, Sir Terence Etherton, and lord justice Sales at one stage dismissed the government’s argument as being “divorced from reality”.

Government lawyers had argued that prerogative powers were a legitimate way to give effect “to the will of the people” who voted by a majority to leave the EU in the referendum. But the lord chief justice declared: “The government does not have power under the crown’s prerogative to give notice pursuant to article 50 for the UK to withdraw from the European union.”

The judgment ruled: “The most fundamental rule of the UK constitution is that parliament is sovereign and can make and unmake any law it chooses ... By making and unmaking treaties the crown [ie the government] creates legal effects on the plane of international law, but in doing so it does not and cannot change domestic law. It cannot without the intervention of parliament confer rights on individuals or deprive individuals of rights.”

The pound surged to a four-week high in the hours after the ruling as investors interpreted it as a sign parliament could put the brakes on any attempt by May to pursue a so-called “hard Brexit” that prioritised controlling immigration over trade with the EU.

Although a related legal challenge failed in Northern Ireland’s high court, the claimants are expected to appeal against that decision, particularly on Brexit’s impact on the devolved legislation. Their claim will be joined at the supreme court hearing with the London case.

Nicola Sturgeon, the SNP first minister of Scotland, said the Scottish government would “actively consider” whether it would formally join in the next legal battle over the right of MPs to vote on article 50, opposing the Westminster government.

The two main claimants in the high court case in London insisted they were not attempting to prevent Brexit. Gina Miller, an investment manager and lead claimant in the case, said: “It was the right decision because we were dealing with the sovereignty of parliament. It was not about winning or losing. It was about what was right. Now we can move forward with legal certainty.”

Deir Dos Santos, a hairdresser and the other lead claimant, said: “Today’s judgment is a victory for everyone who believes in the supremacy of our parliament and the rule of law. I have never challenged the result of the referendum – in fact I voted for Brexit for the sole reason that I wanted power to be returned from Europe to the British parliament. But I did not think it was right for the government then just to bypass parliament and try to take away my legal rights without consulting parliament first.”