As UK's Prime Minister Theresa May wants to start Britain's divorce from the European Union (EU), eleven judges may stand in her way.

On Monday, May's government will ask the justices of the Supreme Court to overturn a ruling that Parliament must hold a vote before Britain's exit negotiations can begin, a case that has raised a constitutional quandary and inflamed the country's heated debate about Brexit.

May plans to trigger two years of divorce talks before the end of March 2017 by invoking Article 50 of the EU's key treaty, using centuries-old government powers known as royal prerogative.

The powers - traditionally held by the monarch but now used by politicians - enable decisions about joining or leaving international treaties to be made without a vote of Parliament.

A hairdresser and a financial entrepreneur, Deir Dos Santos and Gina Miller, went to court to argue that leaving the EU will remove some of their rights, including free movement within the bloc, and that shouldn't be done without Parliament's approval.

Last month, three High Court judges agreed, but the government says they have misinterpreted the law.

Government lawyers led by Attorney General Jeremy Wright will argue this week that the British people have spoken by voting in a June 23 referendum to leave the EU.

In written arguments published before Monday's hearing, government lawyers say the use of royal prerogative to start the talks is "constitutionally appropriate and lawful."

Many legal experts say the government will likely lose its appeal and be forced to give Parliament a vote, but the government was left with little choice than to proceed with the case anyway.

"It's politically problematic, I think, to be seen to not pursue all legal avenues to obstruct this attempt to, in the eyes of some critics, derail the Brexit process," says Jeff King, Professor of Law, University College London.

In a reflection of the constitutional importance of the case - which hinges on the balance of power between Parliament and the executive - all 11 Supreme Court judges will hear the appeal, the first time the full court has sat since it was founded in 2009.

The case is scheduled to last four days, with a ruling likely in January.

Complicating the picture are new participants including the Scottish government, which argues the Edinburgh-based Scottish Parliament should get a vote, too.

Britons voted by 52 to 48 percent on June 23 to leave the EU, but voters in Scotland strongly backed staying in, and the Scottish government says they should not be dragged out of the EU against their will.

London - 1 December 2016

1. Exterior of UK Supreme Court building, traffic on street

2. Close of symbol reading (English): "The Supreme Court"

3. Various exteriors of Supreme Court building

4. Various of Jeff King, Professor of Law, University College London, looking at book

5. SOUNDBITE (English) Jeff King, Professor of Law, University College London:

"Well, I think that there are two reasons probably (why the government appealed the High Court ruling that Parliament must hold a vote before negotiations of Britain's exit from the European Union can begin). The first is that it was very confident that it would win at the beginning, and I think it's reluctant to move from that position of confidence. And secondly, it's politically problematic, I think, to be seen to not pursue all legal avenues to obstruct this attempt to, in the eyes of some critics, derail the Brexit process."

6. Cutaway of King

7. SOUNDBITE (English) Jeff King, Professor of Law, University College London:

"The reaction in some of the media (to the government's loss in the High Court), in particular in the Daily Mail and the Daily Express was, I would say, outrageous. It has been common to criticise judges in the past and I think criticism of judges is perfectly acceptable - they are public officials after all, but this type of language, 'Enemies of the people' (Daily Mail headline the day after the ruling) reminded me of the kinds of things we saw in Nazi Germany."

8. Cutaway of King

9. SOUNDBITE (English) Jeff King, Professor of Law, University College London:

"This is quintessentially a role for judges to play. It's an unclear legal position. The devolved governments don't agree, many members of parliament don't agree. There needs to be an authoritative ruling on what the role of these statutes is in the Brexit process, and that can only be given by a court."

10. Cutaway of King

11. SOUNDBITE (English) Jeff King, Professor of Law, University College London:

"I think that a government loss at the Supreme Court would not derail the Brexit process, but I also think it would be more than a mere speed bump because having to bring forward legislation to give notice would mean that there would be a participation of a much broader range of voices, both in Parliament and in the devolved legislatures and among the devolved governments. And when these voices are heard there is a political obligation of sorts to respond to these voices, to take them into account, to not proceed in a way that ignores them altogether, and I think that will make a difference to the outcome of the Brexit process, but I don't think it will stop it."

12. Cutaway of King

13. Pan of books

14. Various exteriors of Houses of Parliament

A law professor said an appeal of the High Court ruling stating that the British prime minister can't trigger the UK's exit from the European Union without parliamentary approval was unlikely to succeed.

Jeff King, of University College London, said Thursday's comprehensive ruling on an expansive set of grounds could cause the government's argument to fail.

But King cautioned that those hoping for a reversal of the referendum result would likely be disappointed.

London - 3 November 2016

1. Various set up shots of Professor of Law Jeff King, University College London

2. SOUNDBITE (English) Jeff King, Professor of Law, University College London:

"It was very clear, there are many points that rather than just the courts saying that we don't need to rule on this point, the court rather said that we think that point is completely untenable, in some cases suggesting that an argument was divorced from reality. So a court that was very divided on this question might well have given a much slimmer narrower ruling based on very few grounds instead of an expansive set of grounds, dealing with only a few crucial points instead of dealing with many more subtle points, but it chose the latter route. In so it gave a comprehensive ruling on many points, many of which could cause the government's argument to fail. And that gives me confidence that an appeal would be unlikely to succeed under the circumstances."

3. Cutaway of King

4. SOUNDBITE (English) Jeff King, Professor of Law, University College London:

"It may feel that legally there are arguments that it wishes either to make again or to bring new arguments to the attention of the Supreme Court. It may feel that the political consequences of not pursuing the appeal could be problematic, it might be accused of not having followed up every available avenue. These type of accusations are already being made about the pleadings of the government in this very case. So for those reasons, it may have good political and legal reasons to appeal. My sense is that the appeal would be unlikely to be successful. I think that Supreme Court would have even more confidence to be as unequivocal as this court has been."

5. Various of King

6. SOUNDBITE (English) Jeff King, Professor of Law, University College London:

"If that 48 percent (those supporting remain) is hoping this legal challenge will stop Brexit, I think they will be disappointed. I think whether Brexit goes ahead will be a function of where Parliament takes this issue from here. And that's exactly what all the judges in the case were taking pains to point out.''

7. Cutaway of King