The BBC has been urged to appoint a woman as the host of Question Time when David Dimbleby quits the high-profile political show at the end of this year.

Maria Miller MP, the chair of the parliamentary women and equalities select committee, said it was time the discussion programme, which has only ever been hosted by men, took the opportunity to put a woman in charge.

“There’s a great opportunity for the BBC to use their existing women presenters,” she said. “People like Emily Maitlis would make a fantastic follow-up act to David Dimbleby.”

There is substantial pressure among senior female journalists at the BBC for a woman to get the job, following last summer’s equal pay row where it was revealed that many male presenters earned more than their female counterparts. There are also concerns that the appointment process for prominent BBC presenting jobs is not transparent enough.

The delicate game of lobbying to take over as host is already under way, although many potential hosts are reluctant to be seen to be jostling in public for fear they may seem too pushy. In private some raised concerns that simply appearing on a list of potential candidates could make it harder for them to actually get the job.

As a result the appointment process will come under greater scrutiny than in the past, with Tony Hall, the BBC director general, likely to have the final say on who gets the job.

The only person to have openly declared their interest in the job is BBC Front Row host Samira Ahmed, who put herself forward by tweeting:

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.

I've spoken to a senior news manager and been assured that my name is now being passed on for consideration. Happy to go through a process based on equal opportunity, fairness and merit.

Other potential candidates include Maitlis, Kirsty Wark, Emma Barnett, Mishal Husain and Victoria Derbyshire.

Dimbleby’s departure had been seen as an opportunity to rejig the show’s format but Nick Pisani, who edited the programme until 2005, advised against tinkering too much with the show as it already reached a mass audience. He said: “It is the only place where vast numbers of people who don’t follow politics every day watch, have a glass of wine, and throw their slippers at the telly. In that respect I don’t think it should be changed.”

He said that if he was still in charge he would appoint Newsnight’s Evan Davis as host because “he’s got a likeable personality, he’s forensic and popular with the public,” but suggested Desert Islands Discs host, Kirsty Young, was the leading female candidate.

Pisani also advised potential candidates to learn from what happened when the position last became vacant, in 1994, saying: “Dimbleby and Paxman went head-to-head for the job and he got it because he liked the audience. Jeremy didn’t really like the audience and it came across. In the end the whole thing is going to be judged by the presenter themselves, not the format.”