Peter Capaldi, Billie Piper and Karen Gillan call for female Doctor

Writer Mark Gatiss has also said it is the perfect time for an actress to take on the lead role in the show.

Fleabag creator Phoebe Waller-Bridge and Broadchurch star Jodie Whittaker are among the actresses who have been backed for the role.

Capaldi’s decision to step down sparked speculation that the next incumbent could be female after he said he would like to see a woman take his place.

Shortly after announcing his decision he told BBC Radio 2: “The time felt right to bow out, to let somebody else play this wonderful role and I would like Frances de la Tour to be the first female doctor.”

De la Tour, 72, has a 50-year acting career behind her and is best known for playing half-giantess headmistress Madame Olympe Maxime in the Harry Potter films and landlord Rigsby’s tenant Ruth in 1970s comedy series Rising Damp.

Piper, who played companion Rose Tyler, ruled herself out of becoming the first female doctor, saying the responsibility would be “too enormous”, but added her vote would be for Captain America star Hayley Atwell.

Describing her as a “sassy” option, Piper previously told the Press Association: “She would be amazing.”

Meanwhile, Gatiss has said: “I would love it to be a woman, I think it would be marvellous.

“Not through pressure of political correctness but it sort of just feels like it’s time. I think it would just be great.

“The show is not the new kid on the block anymore.

“It’s been back for 12 years and I think it would just be really thrilling, but a lot of people disagree but I just think, why not?”

Gillan, who played companion Amy Pond for two years alongside Matt Smith’s Doctor, has also added her voice to the call, saying: “It would be cool to see a woman in the role one day because a woman could absolutely play that role.”

The 13th Doctor will be announced after the Wimbledon men’s final.