Labour will continue to “defend women’s rights” as it has done for a “long, long time”, Sir Keir Starmer said, as he continued to grapple with his party’s position on trans rights.

Sir Keir, speaking during his regular phone-in on LBC radio, was asked about trans athletes and the success of Lia Thomas, a trans woman who won the 500-yard freestyle title at the women’s NCAA championships.

The victory has sparked a debate around trans athletes taking part in competitive sport, with critics claiming they may have an advantage over other participants.

But Sir Keir said it is for “sporting bodies to decide for themselves” who can and cannot be included in events.

He told LBC the issue “throws up all sorts of difficult questions” but he said Sport England has “crafted quite a careful balance”.

“And it seemed to me that if they could do it, other sporting bodies could probably do it,” he said.

He added: “It probably needs more discussion.”

Labour has found itself in difficulty over trans issues, with Canterbury MP Rosie Duffield both criticised and heralded for her views.

Ms Duffield has come under fire for her opposition to “male-bodied biological men” being allowed to self-identify as female in order to access women-only spaces such as prisons and domestic violence refuges.

She opted not to attend the Labour Party conference in September after receiving threats and being branded transphobic, which she denies.

Sir Keir later said the Kent MP had been wrong to say “only women have a cervix”.

Harry Potter author JK Rowling – who has been vocal on her views on transgender people and biological sex – said earlier this month that the Labour leader could “no longer be counted on to defend women’s rights”.

It came after Sir Keir told The Times “trans women are women” according to statute in the UK, and called for a more “considered, respectful, tolerant debate” about gender.

He insisted he and his party have been defending the rights of women for a “long, long time”.

“I spent a lot of my working life dealing with violence against women and girls first-hand, and I know from that experience just how important it is to fight for women and fight for equality,” he said.

“We have had legislation in this country which makes it clear that, in some circumstances, particularly at the moment under the law when you’ve gone through a process, you can be recognised in the gender of your choosing – that’s been the position for over a decade now.”

Sir Keir said the law needs “reform” but added: “But I equally – I want to be really clear about this – I am an advocate of safe spaces for women.”

Asked if a woman can have a penis, Sir Keir said: “I’m not… I don’t think we can conduct this debate with… I don’t think that discussing this issue in this way helps anyone in the long run.

“What I want to see is a reform of the law as it is, but I am also an advocate of safe spaces for women and I want to have a discussion that is… Anybody who genuinely wants to find a way through this, I want to discuss that with, and I do find that too many people – in my view – retreat or hold a position of which is intolerant of others.

“And that’s not picking on any individual at all, but I don’t like intolerance, I like open discussion.”

Labour frontbenchers Yvette Cooper and Anneliese Dodds both struggled to answer questions on the issue this month.

Shadow home secretary Ms Cooper refused three times to define what a woman is and told Times Radio she was “not going to get into rabbit holes on this”.

Ms Dodds, Labour’s shadow minister for women and equalities, was asked the same question on BBC Radio 4’s Women’s Hour and said there were “different definitions legally” and added: “I think it does depend what the context is, surely.”

No 10, meanwhile, said Boris Johnson believes trans people should be treated with “maximum possible generosity and respect”.

The Prime Minister has “a very clear position” on trans rights, his official spokesman said.

The spokesman was asked whether the PM thought trans women were women, and said people have “the ability to change their legal sex and how that’s recorded”.

He said: “When people want to make the transition in their lives, they should be treated with maximum possible generosity and respect.

“And we have systems in this country that allow it and have done for a long time. We should be very proud of it.

“But obviously you made the point about the importance of the basic facts of biology.”