The quiz show captains Ian Hislop and Paul Merton have faced a backlash over their claims female politicians are too reticent and modest to host Have I Got News For You.

Their comments prompted a surge of calls for gender parity on comedy panel shows, with female comedians challenging the BBC One programme’s producers to “hire us and the MPs will follow”.

Critics accused Hislop and Merton, who were interviewed for the Radio Times, of “mansplaining” the gender ratio on the show. Merton said: “The producers always ask more women than men. More women say no.” Hislop theorised: “On the whole, women are slightly more reticent and think, maybe modestly, ‘I can’t do that’.”

The remarks prompted a hands-up on Twitter from the Conservative MP Anna Soubry, who said she would be delighted to guest host. However, her fellow Conservative Nadine Dorries, a former panelist, vowed never again to appear on the show, describing the format as “too vicious” and “too abrasive”.

Of the 11 politicians to have sat in the host’s chair in the show’s 28-year history, Ann Widdecombe is the only woman. There have been several other female hosts, the most regular being the comedian Jo Brand and the presenter Kirsty Young. 

Deborah Frances-White, a standup comedian and host of the podcast panel shows Global Pillage and The Guilty Feminist, said that far from being reticent or modest, women were “dying to do” her shows – even female MPs.

“This week’s Guilty Feminist episode features the brilliant Stella Creasy MP, who is both high-profile and very funny. Jess Phillips MP was amazing on our suffragette special at the Palladium,” she said.

Any reticence was down to environment, she added. “If panel shows regularly booked at least 50% women, things would change quickly. Being the sole MP among comedians at the same time as being the sole woman among men isn’t very enticing.

“You’d find many fewer male MPs would be keen to come on a show populated entirely by female comedians. There are definitely many exceptional female comics who’d love to do the show. Start there and the MPs will come.”

Catherine Mayer, a journalist, author and co-founder of the Women’s Equality party with Sandi Toksvig, said on Twitter that HIGNFY’s original host, Angus Deayton, “got the job over Toksvig who was told ‘we couldn’t possibly have a woman in charge of the news’.” Toksvig now hosts the BBC Two quiz show QI.

When Jo Brand, who has hosted HIGNFY on 19 occasions, rebuked Merton and Hislop over #MeToo in November, the clip went viral, said Mayer, because it “punctured the whole sniggering schoolboy ethos” of the show.

The late comedian Victoria Wood previously criticised panel shows such as HIGNFY and Mock the Week for being “male-dominated” and “testosterone-fuelled”, while Brand once announced she would never appear on Mock the Week because of its aggressive bear pit atmosphere.

Tiff Stevenson,a standup comedian and actor whose solo show Bombshell is on tour in the UK, has appeared on Mock the Week, 8 Out of 10 Cats and Never Mind the Buzzcocks. Usually she is the sole woman, and she said she felt the burden of the comedian sisterhood on her shoulders. “Suddenly, you are representing an entire gender,” she said. 

If panels were more balanced, “you would be less under the spotlight”, she said. Shows should cast their nets wider and aim for gender parity. “If you are getting a female politician on, then also have a female comedian on.”

Women also faced more criticism, Stevenson said. While men – especially male politicians – “fail upwards”, any woman putting her head above the parapet “is going to have arrows fired at your head”. It had got better, she said, “but it’s still there”. Putting more women on such shows was one solution.

Angela Barnes, a standup comedian, Mock The Week regular and host of BBC Radio 4 Extra’s Newsjack, said the lack of women on such shows meant that while a man might be dismissed as “you’re not funny”, criticism of a woman was just as likely to be “women aren’t funny”. “You have the weight of the reputation of every female performer on your shoulders,” she said.

For women, criticism was not restricted to performance, either. “I don’t think I have ever appeared on TV without at least one person on Twitter commenting on my looks or my weight,” said Barnes.

“Then, of course, there is the abuse. The degrading, often violent, often sexually threatening abuse that is inevitable when a woman puts herself in the public eye. Particularly for female MPs who are currently the targets of some of the most vile behaviour you can imagine.”

In 2014 the BBC decreed that panel programmes without women were “not acceptable” and said things were changing. Barnes said gender parity on panels was the key. “The fact remains that when you enter the game, it simply isn’t a level playing field.”