Here they come, moving fast and breaking things. The roaring boys led by Dominic Cummings and Michael Gove are free to rip up Whitehall, any arm or offshoot of government, and any British institution, with their revolutionary zeal. They have the power: with a majority of 80, who is to stop them?

Where first? The BBC, of course. Boris Johnson made an angry threat to abolish the licence fee, blaming the BBC for reporting the story of the sick child on a hospital floor. Nothing new: the BBC is always in the firing line of the Tory right. The very nature of its being affronts free marketers. Together with the NHS, its fellow national treasure and source of global admiration, it is offensive to ideologues as a collectivist, universal good outside the market. David Cameron chipped away at it, forcing it to accept a £750m cut or take responsibility for stopping free licences for over-75s.

But the assault looks more deadly. Johnson’s ministers are boycotting the Today programme and Treasury minister Rishi Sunak warns that the prime minster has ordered a review into “decriminalising non-payment of the licence fee”, which would cost the BBC at least £200m. Only three years ago the government commissioned a QC to report on exactly that: he strongly recommended against.

Yesterday’s Tory-backing newspapers were packed with anti-BBC fist-shaking: the Times article went under the headline “Boycott threat to punish ‘biased’ BBC”. Its owner, Rupert Murdoch, has lobbied for years to turn the licence fee into a voluntary donation, reducing the BBC to the tiny size of America’s Public Broadcasting Service. The Mail on Sunday devoted page after page to “the absurd distorting mirror of the BBC … now increasingly the megaphone of the liberal elite”.

The revolving door between the BBC and the Tory party suggests otherwise: Guto Harri left to work for Johnson when he was London mayor. Robbie Gibb, who went to the BBC after helping to run Michael Portillo’s leadership bid, rose to become head of Westminster political programmes before leaving to head communications at No 10 for Theresa May. The Today programme is edited by Sarah Sands, former Sunday Telegraph editor. Craig Oliver left as controller of global news to become Cameron’s director of communications in 2011. Andrew Neil, the rottweiler himself, was editor of Murdoch’s Sunday Times and chairs the Spectator. For all their cries of victimhood, the crossover between the BBC and Conservatives is considerably cosier than with Labour. The Tories were especially enraged by Neil’s to-camera attack on Johnson for ducking out of a grilling. But Labour had real reason for outrage at putting Corbyn under that torture without guaranteeing Johnson would get the same treatment.

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All that ammunition might justify the left’s incandescent Twitter-raging against the BBC. Andy McDonald on Today said the BBC “played a part” in Labour’s defeat and Jeremy Corbyn’s vilification: its political editor, Laura Kuenssberg, suffers unrelenting vitriol from the left on social media. The BBC made blunders, and the worst was her reporting Tory spin of a fake “attack” on one of its political advisers. Yet errors are inevitable in 24/7 live coverage, and an apology was instant. I regard her as remarkable for fair judgment, distilling events and arguments with subtlety at speed.

But the bigger question is far harder to answer: is the BBC institutionally biased towards the status quo, against the left? Having worked for seven years in its newsroom as social affairs editor, including during an election, I know that all sides exert ferocious pressure – but by far the strongest muscle comes from the government of the day. And that’s usually Tory. The news agenda struggles not to be dragged behind the front pages owned by maverick far-right barons, many not even UK taxpayers. It’s hard to keep your bearings on basic news values in that cacophony of mendacity. Besides, the right are better bullies.

Play Video 1:25 Johnson says he is 'looking at' scrapping BBC licence fee – video

The BBC tries its damnedest: it self-critiques, analyses and agonises. But of course it can be badly wrong. It was too cowardly during the 2016 referendum, intimidated by Brexit thugs into splitting the difference between their outright lies and the truth: genuine public service required bolder judgments. For far too long it gave climate deniers airtime. Yes-and-no vox pops are excruciatingly meaningless: talk to people, but give time to probe their views.

The BBC can never be good enough, and people will forever shout at the screen. To be the only national arbiter of everything is an impossible burden. But recently it has become infinitely harder. Ofcom’s October report showed that post-Brexit polarisation of a small number of highly politicised individuals, often older, plays a key role in eroding trust in the BBC’s news, by repeatedly highlighting perceived bias on Twitter and Facebook. “People with strong political views generally saw the BBC as too left- or rightwing.” However, five times more people say they trust BBC news than its nearest rival, ITV. It’s where people turn – even the young. The country needs the BBC’s invaluable factcheck in the era of fake news.

Attacks from both sides don’t mean the BBC gets it right. But they do mean the BBC has too few defenders now it is under serious threat from government. Labour is weak and leaderless, but its MPs should imagine life without the BBC. Many on the right are calling for the law to change to allow Fox-style opinionising, calling broadcasting neutrality “old-fashioned”. Look at broadcasting everywhere else to treasure the BBC and its influence.

Consider what phenomenal riches everyone gets for a fee so much cheaper than Sky. Consider that in the cold world outside the European Union, the UK creative industry is one of the few that thrives, because the BBC is its hub for training and production. Netflix is global: most people want to watch British programmes most of the time. As a global ambassador in a friendless world, nothing does more than the BBC.

Challenge it, criticise it, argue with it, but don’t let the marketising right destroy it. Rapid diminution beckons if it is cut and cut again as the licence fee comes up for renegotiation in 2022, or decriminalising non-payment turns it into a voluntary contribution.

Older people in the Midlands and north who gave the Tories their victory watch most BBC. At the weekend, the Strictly Come Dancing final was watched by 11.3 million viewers, His Dark Materials by 9.7 million, Sports Personality of the Year by 8.6 million. What price Fleabag? Whatever people voted for, it wasn’t to destroy one of Britain’s glories. This would be just the first of many things done that they didn’t vote for. Will Labour MPs stand up for the BBC? And here’s an early test for the new Tory benches: with moderates purged, will any of their MPs have the nerve to defend the BBC against the prime minister?

• Polly Toynbee is a Guardian columnist

• This article was amended on 17 December 2019. Craig Oliver was director of communications for David Cameron, not Theresa May. Robbie Gibb was head of communications for May, not for Cameron.