Harriet  Harman has demanded the BBC appoint a woman as the next Doctor Who.

Labour’s former deputy leader, a prominent feminist, also said the new Doctor’s assistant should be a man, so she could ‘tell him what to do’.

But Theresa May – who has said she is a fan of the 54-year-old sci-fi show – hit back, saying the sex of the Doctor was a matter for the programme-makers to decide.

The current Doctor, Scottish actor Peter Capaldi, made the shock announcement on Monday night that he is leaving the TARDIS after three years on the show.

Bookmakers suggest that likely replacements include James Bond star Ben Wishaw and The IT Crowd’s Richard Ayoade.

Twelve actors have played the time-travelling Doctor since William Hartnell first adopted the role in 1963, and so far all of them have been men.

Yesterday Billie Piper, who played the Doctor’s assistant when the show was brought back in 2005, tweeted that it would be a ‘welcome turn’ for a woman to take the role.

Potential female candidates would include Olivia Colman, who was tipped for the job by the 10th Doctor, David Tennant, who starred with her in Broadchurch.

Speaking at a Westminster lunch yesterday, Miss Harman agreed that the next Doctor should be a Time Lady.

‘Of course there should be a female Doctor Who but what we need is a man as her assistant,’ she said. ‘She has got to just tell him what to do, he will need that leadership.’

But the Prime Minister’s spokeswoman said: ‘As someone who has been clear she enjoys Doctor Who, I think she will just want to see it continue and continue to be entertaining. It’s for the programme-makers to decide.’

Mrs May revealed her liking for Doctor Who in an interview with Radio Times about her Christmas Day TV viewing, in which she said: ‘I always like to see Doctor Who on Christmas night, if possible.’

Bookies yesterday named Ben Wishaw, who played Q in the 007 films, as the favourite to become the 13th Doctor.

The 36-year-old has been suggested for the role twice before, when Matt Smith landed the role in 2010 and again when Capaldi took it over.

Rory Kinnear and Rupert Grint have also been named as potentials to pick up the sonic screwdriver.

Last time the vacancy in the TARDIS arose, Mr Whishaw played down the prospect of him joining the show, saying: ‘I don’t think you can be Q and Doctor Who. It would be a bit wrong.’

Announcing his decision to step down from his Time Lord role, Mr Capaldi said: ‘This’ll be the end for me. I feel sad. I love Doctor Who. It’s a fantastic programme to work on.

‘It’s been a huge pleasure to work with… a family. I can’t praise the people I work with more highly.

‘I’ve never worked the same job for three years, and I feel like now is the right time to move on. I’ll still be the Doctor for a while.’

In a statement, show boss Steven Moffatt, who is himself leaving at the end of Series 10 said: ‘Like Peter, I’m facing up to leaving the best job I’ll ever have, but knowing I do so in the company of the best, and kindest and cleverest of men, makes the saddest of endings a little sweeter.’

Broadchurch’s Chris Chibnall, who is taking over from Mr Moffatt, will be given the difficult choice of choosing the next Doctor.

Insiders say it is likely he will choose someone younger who can recreate the popularity that came with David Tennant’s era.

Sales of Dr Who merchandise have fallen in recent years, and producers are keen to boost the show’s popularity with kids.

Some fans feared the regeneration into the 13th doctor could signal the end of the sci-fi show as a 1970s episode said there could only be 12 regenerations.

But thankfully the writers dealt with the problem in the 2013 Christmas Special, when the Doctor played by Matt Smith used all his regenerations up trying to save Trenzalore, the planet it was foretold he would die on.

As his life was set to end, the Time Lords granted him a new generation cycle, allowing the Doctor to regenerate into the 12th Doctor, played by Capaldi.

The BBC confirmed there will definitely be another Doctor.