Eddie Izzard has accused two MPs of “bullying” after they made “transphobic” comments about the comedian, who is campaigning to become a Labour election candidate.

The 60-year-old, launched her bid this month to become Sheffield Central’s MP, told people to “join the 21st century”.

Izzard, who has many connections to Sheffield, having studied accounting, launched her creative career and carried out local activism there, said the city needs “to be bolder, brighter, stronger… on the map”.

Speaking to the PA news agency on Thursday, she said she has been getting “a great reaction in the street” during her campaign but a small minority of people have made transphobic comments.

Earlier this week, Conservative MP Lee Anderson said he “would not follow him into the toilets” if she came to parliament, while Labour MP Rosie Duffield said: “I’m not calling Eddie Izzard a woman.”

In response, Izzard said: “Some people aren’t up to speed, some people haven’t joined the 21st century and, well, they’ve got to get on the bus now because I’ve been out for so long now that I don’t know why they didn’t bring this up before.

“It’s different now that I’m going for a parliamentary seat, but I don’t think bullying is a great thing to be happening and so I’m just going to carry on.”

Addressing Duffield’s comments directly, she said: “Transphobic attitudes come from all different quarters, unfortunately.”

She added that the Labour MP’s comments did not make her feel unwelcome to run as a candidate for the party, but added: “Again, join the 21st century – trans people exist. I exist.”

Izzard said she hopes that being elected will have a “positive impact” for diversity in parliament and for Sheffield Central itself as she brings her global renown, activism and energy to the constituency.

“The fact that I’m trans is kind of by the by,” she said, adding that she “absolutely” thinks people should be focusing on her policies and vision for Sheffield Central.

Izzard is running after the constituency’s incumbent, Paul Blomfield, announced he would be standing down at the next general election.

On Labour’s election prospects, Izzard said new prime minister Rishi Sunak could pose more of a threat and that the party needs to get behind leader Sir Keir Starmer.

“I think it’s going to be tougher for us rather than having Liz Truss in there, but it doesn’t matter,” she said.

“We’re at a certain place in the polls and we’ve got to carry on fighting, and I’m very passionate about getting Keir Starmer in.”

Izzard said she has supported “every Labour leader going”, before stressing the importance of uniting behind a leader to get into government.

“You have to support the leader – that is how it works in politics – and we’re a broad church,” she said.

“We need to be near left and further left – we might agree or disagree on some things but we’re heading in the same direction.”