They say it is a relic in an era of streaming and subscription TV services, like Netflix and YouTube, that consumers can take or leave as they wish. And the penalty falls disproportionately on older people, who are less able to afford the fee, which is currently £154 ($200) a year.

“Quite simply, the world in which the BBC was created, and the license fee was established, has changed beyond recognition,” said Nicky Morgan, Mr. Johnson’s secretary of state for digital, culture, media and sport.

But critics accuse the government of using funding as a weapon to punish the BBC for news coverage it dislikes. The debate over the BBC’s license fee flares regularly, these people say, usually after a new Conservative government takes office and sets about settling scores from the campaign just ended.

The last time the government considered “decriminalizing” the license fee, in 2015 under Prime Minister David Cameron, an independent review estimated it would cost the BBC £200 million a year, around $260 million. Analysts now estimate the cost at between £350 million and £400 million a year, about $450 million to $520 million. That is roughly 10 percent of the BBC’s budget and would force draconian cuts in staff and programming. Any changes would not take effect until April 2022.

“The BBC is the equivalent of BP staring at the Gulf of Mexico before the blowout of its oil rig,” said Claire Enders, a London-based media analyst, referring to the environmental calamity that ultimately cost the British oil company more than $60 billion.

Last month, the BBC announced it would cut about 450 jobs in its news division to prepare for leaner times. That prompted the departure of Sarah Sands, the editor of the Today program on BBC radio, which has been boycotted by the government since last month’s election because of complaints about how its officials were treated on the air.

Mr. Johnson himself spurned an invitation to be interviewed by Andrew Neil, a BBC personality whose forensic questioning of prime ministerial candidates had become an election-year ritual in Britain. Ms. Sands described the prime minister’s strategy as “quite Trumpian: to delegitimize the BBC.”