Martina Navratilova has angered the transgender community by claiming that people who were born male should not be allowed to compete in women’s sports events.

The former Wimbledon champion and LGBT campaigner made the statement on social media, and was swiftly accused of being “transphobic”.

Responding to a question from one of her followers about transgender women in sport, Navratilova said: “Clearly that can’t be right. You can’t just proclaim yourself a female and be able to compete against women. There must be some standards, and having a penis and competing as a woman would not fit that standard.”

She also said: “For me it’s all about fairness. Which means taking every case individually… there is no cookie cutter way of doing things.”

Her comments were seized upon by Dr Rachel McKinnon, a transgender activist and competitive cyclist who this year controversially won a women’s event at the UCI Masters Track World Championship.

Rachel McKinnon with (left) Carolie Van Herrikhuyzen and (right) Jennifer Wagner-Assali credit: Mike Gladu

McKinnon, a Canadian, was born biologically male but transitioned in her 20s. She told her followers that Navratilova was “transphobic” and called on her to apologise, sending a stream of critical tweets.

“Genitals do not play sports. What part of a penis is related to tennis? How does that ‘level’ any playing field?” McKinnon asked.

She also told Navratilova, who won Wimbledon nine times and is regarded by many as the greatest female tennis player of all time: “You realise I’m a world champion trans woman athlete?”

Initially, Navratilova said: “I am sorry if I said anything anywhere near transphobic - certainly I meant no harm. I will educate myself better on this issue but meantime I will be quiet about it.” She also deleted the original tweet.

However, after receiving a stream of critical messages from McKinnon, Navratilova hit back: “Rachel, you might be an expert on all things trans but you are one nasty human being.”

She added that she did not regret her remark and would not be “bullied” into silence, but would bow out of the conversation “because it seems to be my decades of speaking out against unfairness and inequality just don’t count with you at all”.

McKinnon said Navratilova’s record as a campaigner for equality did not excuse her comment. “It doesn’t change the fact that you did something very wrong today. Past good deeds don’t give someone a pass.”

An assistant professor at the College of Charleston in South Carolina, McKinnon told the BBC that she received an estimated 100,000 hate messages on Twitter after winning the championship title.

A picture of her on the podium, dwarfing third-placed Jen Wagner-Assali, fuelled the debate about transgender women in sport. Wagner-Assali said she thought it was unfair that McKinnon was allowed to compete, but later apologised for her comments.

Competitive cycling, as with tennis, falls in line with International Olympic Committee policy which states that trans athletes can compete in their new gender provided testosterone levels are below a certain limit.

McKinnon and other trans activists claim that taking testosterone-blockers and oestrogen as part of the transition process reduces muscle mass, strength and speed and therefore removes any physical advantage. They also argue that being heavier or taller is not necessarily an advantage in many sports.

Navratilova’s friend and former coach is Renee Richards, who was born Richard Raskind and competed in the US Open as a man before having gender reassignment surgery and competing as a woman.

Richards suffered death threats and other players would walk off the court when she appeared, but others including Chris Evert and Virginia Wade did play against her. She now describes herself as a “reluctant pioneer”.

Navratilova ‘came out’ as a lesbian in 1981 and campaigns for LGBT rights. In 2017, she wrote an open letter criticising Margaret Court, the former world number one, for “demonising trans kids and trans adults” by claiming that gender dysphoria was the work of the devil.

Navratilova is also an avowed feminist, saying in one interview: “Of course! How can a woman not be?”