A businesswoman has launched legal action against one of London’s last remaining gentlemen’s clubs, the Garrick, arguing that its men-only membership rules are a breach of equality legislation.

Emily Bendell, chief executive and founder of a successful underwear brand, was looking for a members’ club earlier this year where she could meet people after work, and was surprised to discover that a number of clubs in central London still exclude women.

Disturbed by the continued existence of men-only clubs she contracted lawyers to issue a discrimination claim against the Garrick, which has a central place at the heart of the British establishment, with cabinet ministers, supreme court judges, academics, diplomats, senior civil servants, journalists and well-known actors and writers among its members.

A pre-action letter was sent to the club on Tuesday by Leigh Day solicitors, arguing that the club’s refusal to admit women represents a breach of the 2010 Equality Act. That act allows the existence of single-sex organisations, such as women-only choirs or men-only rugby clubs, but it prohibits discrimination by businesses which provide services to customers.

Lawyers argue that because the club runs a restaurant and guest rooms, it is discriminatory not to allow women to make use of them on the same terms as men.

The letter states: “Only men are able to become members of the Garrick Club and make full use of the services that it provides. Male members are allowed to bring female guests into the club, but women are not able to pay for themselves when they attend, become members themselves, book the facilities that men can book, access certain parts of the club at all, or access exclusive member events.

“In essence, women are only able to access the club’s services as second-class citizens on the whim of a man who has to both invite and pay for them.”

By making it impossible for Bendell to become a member, the club was treating her “less favourably than it has treated or would treat a man who wished to do the same”.

Bendell is seeking an injunction preventing the Garrick from continuing to operate its discriminatory policy, and has requested a response within 28 days.

Acknowledging that some might view this as a niche area of discrimination, Bendell said: “This is a serious issue that needs addressing. I couldn’t believe that these clubs existed, that were men only. I was just really surprised and shocked. If this was a tiny little club with four members in the in the back of beyond, then that would be one thing, but this is a club in the middle of London with QCs and MPs as members – these are people who are running the country. It is really, really concerning.”

She said her frustration at the persistent under-representation of women at the business and investment events she attends helped fuel her desire to take legal action against the club.

Garrick members protest that no networking happens on the premises, and that work meetings are discouraged. They stress that since a large proportion of members are retired, the concern that vital connections are forged here is misplaced. One member described the club as “like an old people’s home with wine”.

Bendell said these arguments were disingenuous. “Even if you don’t talk about work, it’s about having that secret connection because you socialise together. We all know how important these invisible connections are, and in this case women are excluded from this forum. That’s why I wanted to do something about this,” she said.

The club, which was founded in 1831, last voted on whether to include women in 2015, when a majority of 50.5% voted in favour of introducing female membership, however club rules require a two-thirds majority before any change can be introduced.

Members such as the actors Stephen Fry, Damian Lewis and Hugh Bonneville had said before the poll that they were in favour of extending membership to women, as did the then justice secretary, Michael Gove, former justice secretary Ken Clarke and broadcasters Sir Trevor McDonald, Melvyn Bragg and Jeremy Paxman. Three former Conservative MPs and 11 QCs were among those who said they would vote to continue to exclude women members.

An attempt by Bonneville to nominate Joanna Lumley as a prospective member in 2011 failed. This is understood to be the first time an individual has launched legal proceedings against the club.

The former president of the supreme court Lady Hale, who was the first woman among 12 supreme court judges (several of whom were then Garrick club members), has expressed anger at the club’s continued exclusion of women: “I regard it as quite shocking that so many of my colleagues belong to the Garrick, but they don’t see what all the fuss is about,” she told a law diversity forum in 2011. She said judges “should be committed to the principle of equality for all”.

The Garrick Club was approached for comment.