Labour’s shadow women and equalities secretary has said she would not join a London all-male private members’ club which is considering admitting its first female members.

Anneliese Dodds argued the way to achieve equality was to have more women in positions of power and for men to help break down barriers.

The Garrick Club has come under fire after the Guardian published its membership list, which it said included the King, Deputy Prime Minister Oliver Dowden and Levelling Up Secretary Michael Gove.

Sir Richard Moore, the head of MI6, Cabinet Secretary Simon Case and several judges have since resigned from the club, which has repeatedly blocked the admission of women since the 1960s.

Seven women in elite roles have reportedly now been proposed to become the first female members of the club if it agrees to change its rules.

Tory former Cabinet minister Amber Rudd, Channel 4 News presenter Cathy Newman and the classicist Mary Beard are among those put forward to the organisation by a group of current members hoping the exclusion of women will end, according to the Guardian.

Ms Dodds, asked if she would want to join, told LBC Radio on Friday: “Personally, no.

“That’s not really how I would want to spend my time.”

Pointing to the issue of women-led start-ups receiving less financing than those founded by men, the Labour Party chairwoman said: “You need to have more women involved in those decisions about where investment goes.

“But, of course, we could wait for a very, very long time until we got there. So, actually, a big part of the solution has got to come from the men of course, the overwhelming majority of whom, I believe, want to see a more equal future.

“They want to make sure there’s opportunities out there. And certainly in our economy, they know that makes pretty hard-headed economic sense, because if you’re not backing women in our economy, then you’re going to have less growth.

“Surely we’ve got to have both. We’ve got to have women and working-class people, we’ve got to have minority people, we’ve got to have them in those powerful positions. But everyone also has got to be working towards pulling down barriers.”

The management of the Garrick Club, near Leicester Square, is said to be considering new legal advice on whether women should be admitted.