In May 1924, the Manchester Guardian revealed a “recent innovation in the to admit ladies to one of its rooms” meant that the queen of Romania would be lunching at the club during her visit to London. “What would Queen Victoria have said about such a notion!” the article wondered.

A hundred years later, the club’s lethargic advance towards allowing women into the building on equal terms with men continues. On Tuesday, members will once again vote on the matter.

Before the vote, at least nine of the UK’s most senior judges and barristers have parsed the club’s rules to assess whether they do or do not already permit the admission of women.

The former president of the supreme court David Neuberger and the former supreme court judge Jonathan Sumption (both members) have separately written to the club’s chair to inform him that they agree with the legal advice given by the senior lawyer David Pannick KC, who recently concluded that there was nothing in the rules preventing women from becoming members.

Another club member, Edward Henry KC – who is meanwhile representing some of the falsely accused post office operators at the public inquiry into the scandal –disagrees, advising the club: “Unfortunately, David Pannick’s opinion is flawed.”

Members say festering disagreements over the issue are poisoning the atmosphere within the club.

Resignations and threats to resign are rising steadily, with members on both sides of the argument declaring that they will give up their memberships if the vote does not go their way.

The club’s general committee is split, with 13 (the majority) recommending that women should be admitted; this group has written to members warning if the vote fails to admit women they believe “the number who would feel obliged to resign is some 200, and quite possibly more”.

John Simpson, the BBC’s world affairs editor, a member since 2001, : “Various Garrick Club members including Sting, Mark Knopfler and leading actors and producers have reportedly written to the Club chairman saying they’ll resign if the membership doesn’t vote to accept women next Tuesday. Many others like me would also find it impossible to stay.”

Within 24 hours his post had attracted 1,800 responses, many bemused, many ironic (“We would welcome you at the Drones Club. Just the sort of person we need!”; “Just find it weird none of you chaps noticed the absence of women before”; “Why all the fuss about something that only affects 0.000000001pc of the population?”; “What news of the Women’s Institute?”; “Is the Garrick Club like Fight Club!”; “Budge up, Rosa Parks, there are some new changemakers in town” etc.)

The Garrick has come under scrutiny since the of the names of about 60 high-profile members from the club’s closely guarded membership book. The list includes scores of leading lawyers and judges, heads of publicly funded arts institutions, dozens of members of the House of Lords, the deputy prime minister, 10 other MPs, as well as heads of thinktanks, law firms, private equity companies, academics, prominent actors, rock stars, senior journalists and the king.

Details of the strong concentration of senior British establishment figures inside a club that has become notorious for repeatedly blocking moves to admit women drew anger from campaigners for increased diversity in the arts, business, politics and the law.

The letter from 13 committee members noted that the media’s “unfair and unwanted spotlight on the Garrick” had already prompted numerous resignations, including “a number of senior judges, Simon Case, the cabinet secretary, Sir Richard Moore, head of MI6, John Gilhooly, chief executive of Wigmore Hall, and many others, including Downton Abbey producer Gareth Neame, who also resigned as chairman of the Garrick Charitable Trust.”

In his letter to the club chair, Neuberger wrote that he too would resign if women were not admitted, describing the issue as a “running sore” that was becoming a “reputational problem”.

Sumption wrote he had no intention of resigning whatever the outcome, but noted that the ban on women was “indefensible now that women occupy prominent and distinguished positions in every walk of life”.

The arguments of men opposed to the admission of women were “frankly difficult to understand”, he wrote, adding: “I have certainly never heard it said even by opponents that women are, as a group, incapable of being good company. One sometimes hears it said that men are more inclined to show off in female than in male company, but speaking for myself I have never observed that.”

Tuesday’s vote will rest on whether or not members agree that the club’s rules should really be read with the in mind, which suggests that the word “he” should also be understood also to mean “she”, in which case there would be nothing stopping women from joining.

A general meeting of the club will be held at a venue in Covent Garden from 5-7pm where members will debate the issue and vote on whether to confirm a resolution “that the rules of the club allow the admission of women members”; a simple majority of more than 50% will be enough for the vote to pass but several amendments have been tabled aiming to block or postpone a decision to welcome women.

Senior club members opposed to the admission of women have also written a letter, arguing that even if the Garrick was accused of being “old-fashioned or even misogynistic”, members have “the right of free association under the law”.

“It is obvious that, however equal men and women are on every level of intellect and achievement, there are differences between them. It is the most natural thing in the world that both should, from time to time, seek out the special kind of companionship to be enjoyed in places reserved for and, most importantly, run by themselves,” their letter states.

Critics stress that their unease about the Garrick is not based on opposition to men gathering in single-sex spaces, but focused on the high number of powerful men in one organisation that has consistently closed its doors to women.

In a letter to members sent at the end of April, the club’s chair, Christopher Kirker, said the recent media focus had taken its toll and was “very much to be regretted”, but added that he hoped the club would find a “route through the morass that brings us together so that we can return to what makes the Garrick so special: good fellowship, friendship and fun”.

The club has been contacted for comment.