The Scottish and Welsh governments are to be allowed to have a say in the Supreme Court battle over how Brexit should be triggered.
The government is appealing against a High Court ruling that MPs must get a vote on triggering Article 50.
The Supreme Court confirmed that Wales and Scotland's senior law officers will be allowed to take part in the appeal.
UK PM Theresa May said on Friday that work was "on track" to begin the formal process of Brexit by April 2017.
At a joint press briefing with German Chancellor Angela Merkel, following a meeting with EU leaders in Berlin, Mrs May said: "We stand ready to trigger Article 50 by the end of March 2017 and I want to see this as a smooth process, an orderly process, working towards a solution that's in the interests of both the UK and also in the interests of our European partners."
She was speaking after the Supreme Court confirmed that Scotland's senior law officer, the Lord Advocate, had been invited to address the court on the relevance of points of Scots law. The Counsel General for Wales will make arguments about the importance of parliamentary sovereignty and the rule of law.
The Supreme Court hearing is expected to start on 5 December and last four days, with the decision expected in the new year.
Tom Bateman, BBC political correspondent
The government has been clear in its belief that the referendum result gives it the authority to use its executive powers to trigger the EU exit process.
But the Scottish government believes this is unlawful, claiming that invoking Article 50 would involve a "fundamental alteration" in the UK's constitutional arrangements and the rights of Scottish people - who voted to remain in the EU - about which the Hollyrood parliament should be consulted.
It is far from clear how much legal weight these arguments will carry in this complex constitutional case in front of 11 Supreme Court judges.
But the politics are easier to predict: If the government's appeal fails, Parliament is likely to become the next battleground over the timing and - potentially - the terms of Brexit.
It is a fight Downing Street is desperate to avoid - amid the increasingly toxic atmosphere between those tussling for control of Britain's departure from the EU.
A government spokesman said it was "a matter for the Supreme Court which applications to intervene are accepted".
"The UK government's position remains the same, and we will be taking strong legal arguments to court next month," he said.
Scotland's Brexit minister Michael Russell welcomed the decision, but added: "We continue to call on the UK government to drop the appeal and to accept that Parliament has the right to determine the triggering of Article 50.
"We recognise the decision of people in England and Wales to support Brexit, but the views of people in Scotland cannot simply be brushed aside."
The Independent Workers Union of Great Britain, which describes itself as "fighting for the rights and welfare of some of the most vulnerable and under-represented workers in the UK", has also been given permission to make submissions to the Supreme Court.
The Attorney General for Northern Ireland has made a reference to the court on devolution issues and did not need permission to intervene. Separately another Brexit case brought by victims' campaigner Raymond McCord in Belfast has also been referred to the Supreme Court.
Lib Dem opposition
Earlier this month three High Court judges ruled that the prime minister did not have the power to use the royal prerogative to trigger Article 50 of the Lisbon Treaty to start the two-year process of negotiating Brexit, without the prior authority of Parliament.
Mrs May and her ministers are now asking the Supreme Court to overturn that unanimous decision.
Labour has said it will not attempt to delay or scupper this process if a vote goes ahead.
But Lib Dem leader Tim Farron has said his party will vote against triggering Article 50, unless they are promised a second referendum on the UK's Brexit deal with EU leaders. Some Labour MPs have said they are also willing to oppose it.
Scotland's first minister, Nicola Sturgeon, believes that the consent of the Scottish Parliament and the UK's other devolved parliaments and assemblies should also be sought before Article 50 is triggered.
Mick Antoniw AM, Counsel General for Wales, said previously: "This case raises issues of profound importance not only in relation to the concept of parliamentary sovereignty, but also in relation to the wider constitutional arrangements of the United Kingdom and the legal framework for devolution."
The legal challenge over Brexit was brought by investment fund manager and philanthropist Gina Miller, along with London-based Spanish hairdresser Deir Dos Santos and the People's Challenge group, set up by Grahame Pigney and backed by a crowd-funding campaign.
After Lord Toulson's retirement this summer, the appeal will be heard by all 11 remaining Supreme Court justices, led by their President Lord Neuberger.