People should be able to identify as a man or woman “whatever their body parts are”, a shadow cabinet minister said, as Labour remained entangled in a row over trans rights.

Shadow chancellor Rachel Reeves was clearly uncomfortable as she was questioned on an issue which has sparked such bitter feuding that Labour MP Rosie Duffield felt unable to attend the party’s conference in Brighton after receiving threats and abuse.

Ms Reeves said: “I just think that this issue has just become so divisive and toxic, and it pits people against each other – both groups who have faced discrimination in society, women and trans women.

“I just find this debate incredibly unhelpful and unproductive, to be totally honest.”

On Sunday, Labour leader Sir Keir Starmer said it was “not right” for Ms Duffield to have said “only women have a cervix” – a comment which led to claims she was transphobic.

Asked on LBC whether the comment was transphobic, Ms Reeves said: “Is it transphobic? I don’t even know how to start answering these questions.”

Challenged again by presenter Nick Ferrari “is it transphobic to say only women have a cervix”, she said: “I wouldn’t say that.”

She added: “If somebody identifies as a woman or a man, they should be able to do so whatever their body parts are.”

The issue was raised by an activist at a fringe event on LGBT hate crime, who mentioned “a certain MP who really should be asked to stop” and asked what “the Labour Party and its leader should be doing to support trans people”.

Stephen Doughty, co-chair of the LGBT Parliamentary Labour Party, said: “We are absolutely clear where we stand. The Labour Party has clear policies on this.”

He added: “We are raising these issues day in, day out with our colleagues, with the leadership and with others”.

Shadow home secretary Nick Thomas-Symonds said: “If you look at the trans community, over half of them have experienced some form of discrimination. It is absolutely appalling, they are one of the most discriminated against communities.

“We stand in solidarity with them, we have a firm policy.”

Northumbria Police and Crime Commissioner Kim McGuinness said: “I don’t like to see discourse like that in the Labour Party.”