Rishi Sunak has intervened in a row between Kemi Badenoch and actor David Tennant, saying the Doctor Who star is “the problem”.

Tennant suggested at the British LGBT Awards last week that he wanted a world where the equalities minister “doesn’t exist any more”, and said she should “shut up”.

The prime minister posted on X that freedom of speech was the “most powerful feature of our democracy”, adding: “If you’re calling for women to shut up and wishing they didn’t exist, you are the problem.”

Trans rights campaigners have criticised Ms Badenoch’s views on gender.

Tennant won a prize for being a “celebrity ally” at the awards show and used his speech to criticise Equalities Minister Mrs Badenoch.

In his acceptance speech he said: “If I’m honest I’m a little depressed by the fact that acknowledging that everyone has the right to be who they want to be and live their life how they want to live it as long as they’re not hurting anyone else should merit any kind of special award or special mention, because it’s common sense, isn’t it?”

He said it was “human decency”, adding: “We shouldn’t live in a world where that is worth remarking on.

“However, until we wake up and Kemi Badenoch doesn’t exist any more – I don’t wish ill of her, I just wish her to shut up – whilst we do live in this world, I am honoured to receive this.”

Mrs Badenoch responded to the comments on Tuesday, posting on X: “I will not shut up. I will not be silenced by men who prioritise applause from Stonewall over the safety of women and girls.

“A rich, lefty, white male celebrity so blinded by ideology he can’t see the optics of attacking the only black woman in government by calling publicly for my existence to end.”

She said Tennant was one of Labour’s supporters and was “an early example of what life will be like if they win”.

“Keir Starmer stood by while Rosie Duffield was hounded,” she said. “He and his supporters will do the same with the country.

“Do not let the bigots and bullies win.”

But Labour candidate Dawn Butler said on X: “Not all black women think the same. I agree with David Tennant.”

• Who can I vote for in the general election?

Labour candidate Rosie Duffield announced earlier this month that she had withdrawn from hustings events because of the “constant trolling, spite and misrepresentation”, which she said was “being pursued with a new vigour during this election”.

Ms Duffield has said there should be protected spaces where those born male are not allowed to go, such as domestic violence refuges and prisons, and she is against people being able to self-identify as trans to gain access to those spaces.

She has previously faced death threats and multiple instances of abuse over her stance on sex and gender.

You can find a full list of candidates for North West Essex, Brent East and Canterbury on the BBC News website.