The High Court is to rule on whether the government can begin the formal process of leaving the European Union without consulting Parliament.
Senior judges heard a challenge last month from campaigners who argue Prime Minister Theresa May does not have the power to invoke Article 50 of the Lisbon Treaty without MPs’ approval.
The PM has promised to trigger Article 50 by the end of March 2017.
Judges are set to give their verdict at 10:00 GMT.
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Some of the leading figures in the legal world are involved in the historic case, which is expected to be appealed against to the Supreme Court whatever the verdict.
The announcement will be made by Lord Chief Justice Lord Thomas, Master of the Rolls Sir Terence Etherton and Lord Justice Sales.
The government insists it does not need to consult Parliament before triggering Article 50, which begins two years of formal Brexit negotiations.
It argues there is an established constitutional convention for the executive to use ancient powers of royal prerogative to withdraw from international treaties – and that the referendum result has given ministers the green light to begin Brexit.
But the claimants – led by investment manager Gina Miller – argue that rights granted by the 1972 European Communities Act cannot be taken away without the explicit approval of Parliament.
A number of MPs have also been calling for Parliament to be given a vote before Article 50 is triggered, saying the government has no mandate to decide the terms of Brexit.
But Mrs May has said their demands are akin to trying to “subvert democracy”.
The government has said it is likely MPs will get to vote on the final Brexit deal reached after the negotiations – but campaigners say this is too late.
The prime minister has refused to give details of her key demands for the talks.
Among those calling for Parliament to be given a vote is the Scottish peer who wrote Article 50.
In a BBC interview, Lord Kerr of Kinlochard said he believed Article 50 was “not irrevocable”, adding that the UK could choose to stay in the EU even after exit negotiations had begun.
Meanwhile the head of the civil service, Sir Jeremy Heywood, said it might be decades before the full impact of the referendum result on the UK was known.
Setting out the challenge facing Whitehall in his blog, he said Brexit had “few, if any, parallels in its complexity”.
He also defended the civil service’s role during the referendum campaign, when Brexit-supporting ministers were barred from seeing some documents under special rules allowing members of the government to campaign for either side.
“During the official referendum campaign, we were scrupulous in making sure that all documents issued were factually correct and objective,” he said.
Exiting the EU will involve almost every government department and thousands of civil servants, he said.
Brexit: High Court judges to give legal verdict}