On Tuesday, after Johnson accepted the European Union’s offer of a further delay to the Brexit process, a Tweet from the show’s popular Twitter account said: “As UK heads into third Brexit extension, country looks forward to another three months of bickering, amateur dramatics and absolutely nothing being achieved before asking the EU for another one.”

Hislop, one of the captains, dismissed the idea that the show was behind Johnson’s success. “If we ask someone on and people like them, that is up to people,” he said in a telephone interview, pointing out he had never given Johnson an easy ride.

(In a 2014 TV documentary about Johnson, however, Hislop said, “There is a sense of guilt that part of Boris’ success has been built on his performances.”)

The show had been blamed for the rise of politicians on the left too, Hislop said. He expected criticism soon if Jess Phillips, another popular guest, became leader of Britain’s Labour Party. “If in 10 years’ time, the country is falling apart due to the fact Jess Phillips has moved violently to the left and totally screwed everything up, there will be people who’ll say, ‘She’s only popular because she was on “Have I Got News for You,”’” he said.

Jimmy Mulville, co-founder of Hat Trick Productions, the company behind the show, said he didn’t lose sleep over Johnson’s or Rees-Mogg’s rise. If anything “gives me cause for concern” about the show, he said, it was when politicians have used it to rehabilitate their public image. Alastair Campbell, Tony Blair’s former spin doctor who was accused of beefing up the case for Britain and America to invade Iraq, had done just that, Mulville said.