The prime minister’s bonhomie with Leo Varadkar after their talks in the Wirral last Thursday took many by surprise. It must have come as a particular shock to readers of the Times, who just 24 hours earlier had been told that the taoiseach had “reneged on a secret deal with Boris Johnson to open the way to a Brexit compromise”. And the source of this story? An unnamed Downing Street insider.

It’s been quite a run for “No 10 source”. In barely a week, the increasingly ubiquitous attribution was behind reports that the normally stolid Angela Merkel had accused Johnson of trying to play a “stupid blame game”, and the news that European states seeking to stymie the prime minister’s Brexit proposals would go to the back of the “queue” for future trade deals.

The more journalists report unsourced claims, the less government will engage on the record

What will No 10 source reveal next? That “Corbyn has promised to sell Northern Ireland to Brussels”? That Johnson is “the best prime minister ever”?

This is not how anonymous sourcing is supposed to operate. Whistleblowers and leaks are a vital part of journalism. Without them we would know far less about how government and powerful organisations work. Richard Nixon would have seen out two terms as US president. The law firm Mossack Fonseca would still be hiding the super rich’s secrets in Panamanian bank accounts.

But when the government is able to use the convention of blind quotes to regularly set the news agenda, something has gone wrong.

The growing reliance on anonymous briefings allows Downing Street to push narratives without having to take responsibility for them. Rasmus Nielsen, director of the Reuters Institute for the Study of Journalism, has said that British journalists are being “played like an instrument” when they publish stories based on government leaks and anonymous sources. There is also no way for proper public scrutiny to be placed on such a source.

The more journalists report unsourced claims, the less the government will engage on the record. Why put up a minister up for a potentially combative live interview when, as happened last week, BBC Radio 4’s World At One programme reads out on-air a lengthy text sent from an anonymous No 10 source to a magazine journalist? The “leak”, originally sent to the Spectator, set up the prime minister as the custodian of the supposed will of the people against a pernicious European Union. Not exactly Deep Throat – more like Classic Dom.

Dominic Cummings arrived in Downing Street as Boris Johnson’s special adviser, promising zero tolerance on leakers. Now many believe he has become the (very) thinly veiled source of a series of government announcements by anonymous briefing – this both gives Johnson plausible deniability when the kites being flown hit overhead wires, and adds to the mythology of Cummings as the éminence grise playing multi-dimensional chess.

Government spinning stories is hardly new. Margaret Thatcher’s press secretary, Bernard Ingham, frequently briefed the media to settle internal party scores. Alastair Campbell was so successful at controlling the press that he became immortalised in The Thick of It.

But, as with everything else, the internet has changed the rules of the game. Many of the biggest news mornings since Johnson took office have begun not with a set-piece interview – as was long the case – but with a tweet thread from a prominent journalist setting out the government’s key talking points for the day. There is no space for rebuttal. By the time scrutiny arrives, hours or even days later, the message is already out.

Boris Johnson’s special adviser Dominic Cummings. Photograph: Peter Summers/Getty Images

Increasingly, politicians do not even need to go through journalists. They can speak directly to their intended audiences through social media, confident that sympathetic titles and reporters will rush to repackage their statements – and if they don’t, there won’t be any more “exclusive” stories heading their way.

It’s a textbook example of what American linguist George Lakoff calling “framing the narrative”. What journalists are talking about matters more than whether it is true or false.

Donald Trump is the master of narrative framing – though he doesn’t need anonymous briefings to do it. From “crooked Hillary” to his comments about the Kurds not fighting in Normandy, the US president has long shown how to use the “he said, she said” conventions of reporting to spread disinformation. Even debunking false or inaccurate claims gives misinformation more oxygen, paradoxically lending it credibility.

This poses a huge challenge for journalism. The New York Times was heavily criticised recently for a front-page headline that declared “Trump Urges Unity vs Racism” after a spate of racially motivated attacks that the president was widely accused of having stoked with his inflammatory rhetoric.

There are plenty of signs that Johnson has read Trump’s script. The anguished howls from anti-Brexit campaigners when he erroneously blamed “Brussels bureaucrats” for British kippers being transported on “ice pillows” only served to amplify the core anti-EU message.

The traditional standard of objectivity in journalism is often parsed as “reporting what everyone says without fear or favour”. But what if you are reporting something that is misinformation, or even a flat-out lie? And beyond the more blatant misdirections of Trump – and Johnson – it is even harder to judge this when readers aren’t even told the exact source of information.

Brexit has revealed the limits of Westminster lobby journalism and its susceptibility to narrative framing. Fearful that audiences will switch off in the digital age, journalists have often treated Britain’s departure from the EU more like a melodrama populated by colourful characters than an intricate, complicated policy story. In this febrile atmosphere, journalists have been drawn into reporting leaks without interrogating the substance behind the story.

What’s the solution to all this? Being more honest with audiences about where stories come would be a start – and providing far more context about the potential motives of their source. Journalists could be far more selective in reporting what is said inside government when it doesn’t come with an official attribution.

Trust in journalism has been badly shaken over the last decade. Just adding “government source” at the end of the first paragraph is not enough. Readers are not stupid. We shouldn’t act as if they are.

• Peter Geoghegan is investigations editor at openDemocracyUK