The culture secretary has called on the BBC to appoint a woman to replace David Dimbleby as the host of Question Time.

Dimbleby, 79, who has chaired the most high-profile British political TV show for 25 years, announced this week he would step down in December, sparking widespread debate over who should take over the role.

During questions to the digital, culture, media and sport secretary in the Commons, Vicky Ford, the Conservative MP for Chelmsford, asked Matt Hancock’s view on Dimbleby’s replacement.

“Does he agree with me that in this year, 100 years of women’s suffrage, this baton should be passed to a woman?” she said.

Hancock replied: “While of course the job must go according to merit, I think it’s about time that we had a woman at the helm of Question Time.”

The calls for the coveted Question Time role to be given to a woman come as the BBC has pledged to address issues including gender inequality over pay and on- and off-screen opportunities.

The race to replace Dimbleby has opened up fierce competition among the potential candidates, with Samira Ahmed, the journalist and presenter of Radio 4’s Front Row programme, using Twitter to throw her hat in the ring and state her credentials.

"I have 2 awards for journalism, 28 years in the broadcast news biz, including 11 at C4 News, currently presenting @newswatchbbc & @BBCFrontRow & an honorary fellow of St Edmund Hall, Oxford. I'm v well qualified to present @bbcquestiontime & I'd like to be seriously considered."

Other leading internal candidates include the Newsnight presenters Emily Maitlis and Kirsty Wark, the Radio 4 Today programme hosts Nick Robinson and Mishal Husain, and Desert Island Discs’ Kirsty Young.

The BBC could choose to go for a more left-field choice such as Victoria Derbyshire, whose morning news show on BBC Two has won a series of awards, or the Radio 5 Live presenter Emma Barnett, who received plaudits after standing in for Andrew Marr on his Sunday programme this year.

Outside the BBC, the Channel 4 News anchor Krishnan Guru-Murthy has been speculated as a potential candidate.

Dimbleby is one of only three presenters to have hosted Question Time since it was first broadcast in 1979. The others were Robin Day and Peter Sissons.

The current host has gained a cult following during his time on the programme, attracting parody Twitter accounts and even dancing competitions. “I do know there’s a Dimblebot and there’s a Dimbledance and I can do it too,” he said on the show in 2011.

Dimbleby has only ever missed one episode of the show, when he was admitted to hospital after being kicked by a cow at his Sussex home in 2009.