Around 1,400 people have contributed more than £50,000 to the People’s Challenge, meaning the group has hit its first funding target to prepare a written case for the High Court, The Press Association reported.
Crowd-funding organiser Grahame Pigney insists there is a need to “fight suits with suits” and is seeking to raise a further £100,000 to boost the campaign’s legal team in court, adding that he is open to Brexit backers joining his cause.
Mr Pigney argues that the Prime Minister needs an Act of Parliament to trigger the two-year process of negotiating the UK’s withdrawal from the EU.
Government lawyers advised in July that the royal prerogative can be used to invoke Article 50 of the Lisbon Treaty - which does not require a vote in Parliament.
Mr Pigney, of the Say Yes 2 Europe group, is joined by his 22-year-old son Robert, Gibraltarian national and Brex-In founder Paul Cartwright and others in developing the legal challenge.
Speaking from France, 62-year-old Mr Pigney told the Press Association: “What we’re doing is on behalf of everybody - not just experts, not just on behalf of a few people interested in this, but 65 million citizens in the UK.
“They all have these rights. Whether they use them or cherish them, they all have these rights and Parliament needs to make the decision rather than the Government in some sectional, political interests.
“I don’t see why Leavers can’t get behind this as it’s about parliamentary sovereignty.”
Judges have decided a legal challenge over Brexit can be heard by the High Court in October, with London-based investment manager and philanthropist Gina Miller the lead case in the action.
The legal action has been described as “the most important constitutional law case in living memory”, with the People’s Challenge aiming to be involved as an interested party.
Mr Pigney, who lives near Carcassonne and was unable to vote in June’s referendum after moving to France 19 years ago, is vocal in his backing for the EU and frustration at the referendum result.
But he adds that his legal bid is about allowing MPs to decide what happens next.
This approach could be a source of frustration for Brexit supporters by adding to their fears that either the UK will not trigger Article 50 or a watered-down approach will be adopted, given that the majority of MPs backed Remain.
Mrs May has developed the slogan “Brexit means Brexit” as she seeks to reassure fellow Tory MPs about her commitment to honouring the referendum result despite opting to back Remain.
Mr Pigney said he could not deny that he would like the referendum result “ignored” and for people to be allowed to have a chance to “make a more informed decision”.
But he also said: “If Parliament decides we leave the EU, I cannot argue with that. It’s the democratic process. I don’t want that to happen. I would like Parliament to have a long, hard think and come to a more sensible conclusion.
“If Parliament decides it’s going to take us out and set the conditions and timing, I cannot argue with that.
“I can argue with Theresa May saying ‘Brexit is Brexit’, which is as useful as her saying ‘Breakfast is breakfast’.”
Mr Pigney, who said his background includes working in IT, suggested MPs need to take “account” of the referendum result, noting: “The referendum was, in effect, a Parliament-organised opinion poll. Parliament has to take it into account.”
Conservative MP Bernard Jenkin, chairman of the Public Administration and Constitutional Affairs Committee, said of the legal challenges: “This is ludicrous, it’s desperate and it’s people who cannot face the truth that Britain’s membership of the European community has lost democratic consent and that’s what counts.”
Ukip MP Douglas Carswell suggested those pursuing cases against how the EU referendum result is delivered are “out of touch”.
He said: “It’s very clear as a point of law that the Government can trigger Article 50 without a vote in the Commons.
“The issue is whether or not judicial activists try to subvert the referendum result despite the fact that the law is crystal clear.”