Legal experts say it is one of the most significant – and consequential – tests of Britain's constitution in decades. The royal prerogative is a fading relic of the age of kings and queens – these days even a decision to go to war may go to parliament.

But the government is determined to defeat what it calls an attempt to find a "back door" out of Brexit. It has accused the woman who brought the case of "seeking to undermine democracy".

Businesswoman Gina Miller, co-founder of investment fund SCM Private, has received death threats and been accused of treason after leading the legal challenge against prime minister Theresa May's right to single-handedly trigger Brexit.

The 51 year-old says she has been told "my head belongs on Traitors' Gate', the infamous arch leading into the Tower of London.

"Our business has been boycotted," she told AFP. "It's been quite vile. But I won't be bullied because to my mind this is best for everyone, to have legal certainty".

Her business, like many financial firms in London, would be hurt by a 'hard Brexit' that ended financial passporting into European markets.

Protesters gathered outside London's faux-Gothic Royal Courts of Justice on Thursday, dressed in legal wigs and gowns with signs saying "Lawyers, hands off our democracy!"

They handed out leaflets saying the Brexit vote had been "the biggest democratic mandate in British political history and it must be respected".

Before the High Court Mrs Miller was represented by Lord Pannick QC, one of the UK's star barristers.

Lord Pannick has been called "the best advocate of his generation". He appeared for the Sunday Times in the Spycatcher case in the 1980s – a sequel to the Australian case which starred a young Malcolm Turnbull.

More recently, he persuaded the European court of human rights that the News of the World had breached former Formula One boss Max Mosley's privacy, and in the future the media must warn people before exposing their private lives.

Lord Pannick told the court the case "raises an issue of fundamental constitutional importance".

Quoting case law from as far back as the 17th century, he argued that if the prime minister triggered Brexit then it would remove the rights of citizens that had been established by an act of parliament.

The royal prerogative cannot be used to deprive people of rights which they enjoy in domestic law, he said, quoting a legal decision from 1610 when the House of Commons was fighting King James I over his ability to make proclamations without legislation.

Lord Pannick denied that the case was "merely camouflage" for a political attempt to reverse the Brexit referendum result.

"Of course my client, Mrs Miller, wishes this country to remain a member of the EU… but that is not the issue in these proceedings," he said.

"If we are to leave the EU then the steps to be taken which will deprive her of (her) rights… must be taken in a lawful manner."

Mrs Miller's legal claim was "in support of parliamentary sovereignty", he said.

Once Mrs May had "pulled the trigger" on Brexit under Article 50 of the European treaty then "the bullet hits the target… and that has a dramatic impact in domestic law".

Attorney-general Jeremy Wright QC MP will defend the case on behalf of the government – he is due to present his arguments on Monday.

In his 'skeleton argument' he told the court that the case "seeks to undermine democracy because (it) ignores the wishes of the people".

In a statement issued in September, he said "The country voted to leave the European Union, in a referendum approved by Act of Parliament. There must be no attempts to remain inside the EU, no attempts to re-join it through the back door, and no second referendum.

"We do not believe this case has legal merit. The result should be respected and the Government intends to do just that."

Lord Pannick said it was expected there would be a decision before Christmas.

But experts expect the case to be reviewed by the Supreme Court, no matter what the result.