Transgender swimmers, who were born biologically male, have been allowed to swim in the lake under informal guidance since 2019.

Campaigners argue that these rules are unlawful following the Supreme Court ruling in April that biological men should not have access to women-only spaces..

One woman said: “I was showering outside after my swim when a big man with a long wig and a long coat came walking down the path to the pond area.

“This man came and lingered in the restricted area between the outdoor showers and the fence, where my towel was draped.

“He stood there turned at an angle, looking at me and evidently wanting me to know that he was looking at me.

“I was trapped, because I was naked and my towel was on the fence behind him.”

Women’s rights protesters have protested at the site, including entering the men’s pond wearing false beards and moustaches in recent years.

The objections have only intensified since the Supreme Court ruled in April that the definition of a woman is based on biological sex for Equality Act purposes.

This landmark ruling provides legal backing for organisations to protect single-sex spaces like changing rooms.

Following the decision, Sir Keir Starmer said that organisations refusing to implement the ruling must do so “as soon as possible”.

Sex Matters argued that “The Ladies’ Pond is not a single sex facility … precisely because trans women are permitted to access the swimming facilities.”

Maya Forstater, chief executive of Sex Matters, said: “We were amazed to discover that the City of London Corporation thinks the Ladies’ Pond is not a ‘single-sex service’ in law. This is nothing more than linguistic trickery.

“The corporation claims that, because it chooses to define ‘women’ and ‘men’ according not to biological sex but to who wants to be referred to as ‘she’ or ‘he’, the Supreme Court judgment doesn’t apply.

“Neither Hampstead Heath nor the City of London Corporation are sovereign entities that get to make their own laws.

“We will be taking our next steps in August and think this case will be very significant in testing what can only be described as creative interpretations of equality law following the Supreme Court judgment.”

The Kenwood Ladies’ Pond Association (KLPA), a volunteer-led group representing people who use the pond, said: “The Ladies’ Pond is open to all women and girls over the age of eight and, according to the lifeguards, trans women have been swimming there for many years without incident.

“The Ladies’ Pond is well-staffed by lifeguards and stewards who are there to ensure the safety and well-being of all users.”

Last year, a motion that “only those born female in sex can use the pond” was “resoundingly defeated” by members.

Hampstead Heath has about 30 ponds, which are fed by natural springs and attract more than 750,000 visits each year.