A key legal challenge over whether Prime Minister Theresa May has the power to start the UK's withdrawal from the European Union (EU) without parliamentary approval has begun today (13 October).

A group of claimants led by investment manager Gina Miller and hairdresser Deir Dos Santos are demanding that the triggering of Article 50 – which starts a two-year deadline for the exit process to be completed – be subject to a vote in parliament. The case will be settled by a three-day judicial review in the Royal Courts of Justice.

Miller is being represented by Mishcon de Reya, which has instructed a group of heavy-hitting barristers including Blackstone Chambers' David Pannick QC, widely regarded as one of the country's leading experts on constitutional law. Mishcons' London headquarters have been targeted by protesters opposed to the legal action.

Dos Santos, meanwhile, is being represented by David Greene, senior partner and head of group action litigation at London law firm Edwin Coe, and Dominic Chambers QC, a commercial law barrister at Maitland Chambers.

UK attorney general Jeremy Wright QC is representing the government alongside James Eadie QC, one of the government's lead advocates in civil litigation.

Miller and Dos Santos are joined in the action by a number of interested parties and interveners, including The People's Challenge, which has used crowdfunding to finance the case, raising almost £160,000 from around 4,500 supporters.

The People's Challenge is being represented by John Halford, co-head of public law at London law firm Bindmans, which is known for its work on civil liberties and human rights, and Helen Mountfield QC of Matrix Chambers. The crowdfunding was organised by Grahame Pigney, a British expat living in France who is part of the pro-EU campaign group Say Yes 2 Europe. "The enforced removal of citizenship rights from 65 million people is completely unprecedented in a modern democracy," Pigney says on the fundraising page.

A separate crowdfunding by Devereux Chambers' Jolyon Maugham QC raised more than £10,000 to pay for legal advice from public law experts.

The group secured an early win a fortnight ago, with a High Court judge ruling that the government release its private legal arguments for not consulting parliament on the triggering of Article 50. The documents revealed that government lawyers will argue it is "constitutionally impermissible" for parliament to be given a vote on the Brexit process. "It is a polycentric decision based upon a multitude of domestic and foreign policy and political concerns, for which the expertise of ministers and their officials are particularly well-suited and the courts ill-suited," the documents say.

Miller's skeleton argument argues that triggering Article 50 without an act of parliament would "substantially undermine" constitutional rights. It also says that May's recent announcement that she will trigger Article 50 by March puts her on a "collision course" with the courts by effectively "pre-empting the outcome of the case".

May recently conceded to demands from rival parties for parliament to hold a "full and transparent debate" of the government's Brexit plans before the formal exit process begins, but stopped short of pledging a parliamentary vote on Brexit negotiations or the triggering of Article 50.

The requirement for the UK's withdrawal from the EU to be subject to an act of parliament has widespread support within the legal industry. More than 1,000 UK lawyers previously wrote to former Prime Minister David Cameron to demand that MPs vote on the triggering of Article 50.