Given Boris Johnson’s hefty majority in Westminster, there wouldn’t appear to be an obvious business opportunity for a new conservative media brand dedicated to challenging the orthodoxy.

Yet The Critic defies easy categorisation. If the prime minister was expecting a friendly addition to the Tory newsstand alongside his previous employers, The Daily Telegraph and The Spectator, he was in for a big surprise.

In The Critic’s debut edition, writer Jonathan Meades referred to Johnson as “the shit”, not to mention “an antinomian, boorish, cosmically embarrassing charlatan”. In the centre spread, artist Adam Dent illustrated a map of “Johnson’s London” – Boris, not Samuel – with references to the prime minister’s late-night row with his girlfriend in Camberwell, his sacking from The Times in Wapping and numerous other political and carnal adventures across the capital.

Now four editions in, The Critic bills itself as “the new Magazine for open-minded readers” (it’s also a website).

The venture is being underwritten by Jeremy Hosking, a Brexiteer investment tycoon who happens to be one of Britain’s leading collectors of stream trains. It is another home for some well-established writers on the right, such as David Starkey, Simon Heffer, Peter Hitchens and Anne McElvoy. But publisher and co-editor Michael Mosbacher wants to be a maverick. “It’s very much not meant to be doctrinaire, pushing one particular line.” Taking Hosking’s money does not equate to being his mouthpiece, he insists. “He’s a strong Brexiteer, Eurosceptic and right-of-centre, but we are not trying to fit into that narrowly.”

On its website, The Critic states its raison d’être as “to push back against a self-regarding and dangerous consensus that finds critical voices troubling, triggering, insensitive and disrespectful”.

Most obviously, it exists as a counterweight to some of the identity politics expressed on social media. But some of its most obviously liberal-baiting output would probably delight Downing Street guru Dom Cummings, far less ruffle establishment feathers.

For example, the magazine has run a piece criticising a new Australian law banning hikers from climbing Uluru (Ayers Rock), a sacred site for Aboriginal people. It published an attack by Toby Young on the concept of ‘white privilege’, which he claims is a “myth” and “poisonously racist”. And it suggested that big game trophy hunting in Africa is a good thing (Mosbacher notes the prime minister has recently become a champion of animal rights).

Speaking in a cafe near to The Critic’s Westminster office, Mosbacher says the magazine is engaged in “culture wars” and in fighting “consensus” thinking which has become louder and more agile with the internet. “[Social media] has changed the pace. There’s more screaming,” he says.

He is keen to take on groupthink in the arts world. The Critic ran Norman Lebrecht’s withering assault on London orchestras which remain viable only by jetting off to do foreign concerts “at the drop of a Luxembourg invitation”. It published DJ Taylor’s view that the literary press has drawn in its teeth and that books are “not so much reviewed as endorsed”. Artist Alexander Adams dismissed liberal icon Banksy as a “talented graphic designer with a talent for self-promotion”.

During the interview, Mosbacher is joined in the cafe by co-editor Christopher Montgomery, who was previously an architect of Brexit as a strategist for the ERG faction of hardline Eurosceptic Tory MPs. Before that he was chief of staff for the Democratic Unionist Party.

Montgomery rejects the idea that The Critic might feel like a rejection of the fast-changing modern world by a group of ageing (mostly male) writers. “There is no new emerging youth consensus,” he insists. “There is a youth consensus as imagined 40-50 years ago which has become received orthodoxy which nobody can break away from.”

He notes that “OK, Boomer” – the social media put-down used by millennials in arguments with baby boomers – could easily be directed at many of those running the UK’s media. “What the hell does Tony Hall know about what young people are thinking? Was it all the young people he met as trustees of Covent Garden?” he says (speaking before the BBC director general and former chief executive of the Royal Opera House revealed his plans to leave the broadcaster and chair the board of the National Gallery). Montgomery cites a scathing review of Hollywood’s recent reimagining of Charlie’s Angels as evidence that The Critic is not divorced from topics that engage a younger audience.

Mosbacher is well aware of the difficulties it faces in having a long-term future. “In the short term it won’t be profitable, it’s an expensive undertaking,” he admits.

In its debut edition The Critic published a “good luck” message from David Goodhart (author and founder of Prospect, one of The Critic’s rivals in the monthly periodicals space). “Does the world need another magazine of tastefully-written, somewhat contrarian, conservatively-inclined thinking? Probably not,” he posited. But with “some luck and some scoops”, it might find “a little foothold” among “the writing and reading classes”, he suggested, by way of encouragement. Provided “the funding doesn’t run dry”.

Mosbacher claims that Hosking, who runs the magazine through his company Locomotive 6960 (named after a steam train he owns), is a hands-off proprietor. “He doesn’t interfere at all. I find him very straightforward to work with.”

He says that the long-term business model is based on building a subscriber base of 15,000, which he argues are the “real subs figures” of others in the market, after bulk sales and doubly counted digital/print subscriptions have been subtracted from official ABC circulations. The Critic’s website is open access but only temporarily. “The model will be that as our name goes out there and subscribers go up we will introduce a metered paywall and gradually ratchet that up.”

Launching a print title for the third decade of the 21st century might seem counter-intuitive but Mosbacher says that a digital-only product would struggle to get noticed. “It would just be seen as another web project,” he says. “Having a title, where you can go into WHSmith and see it on the newsstand, means it stands out.” He references Tortoise, the digital journalism platform founded by former BBC News director James Harding with millions in investment funding. “It hasn’t had the impact that they would have hoped,” Mosbacher claims.

The sub-plot to The Critic’s launch is that it will go head-to-head with Standpoint, the magazine which Mosbacher used to edit and was involved with from its founding in 2008. The two titles sit alongside each other on the newsstand, both priced at £5.95 and often fishing from the same pool of writers.

Mosbacher’s explanation of the schism is that Hosking had been willing to put money into Standpoint if it was prepared to run more of “the culture wars content” that interests him. Some of Standpoint’s board (which includes MPs Michael Gove and Frank Field, playwright Tom Stoppard and painter David Hockney) “weren’t happy with that”, he says. Mosbacher was convinced that a magazine could not flourish “without a big injection of money”, so he went off with Hosking to set up The Critic.

It must establish itself in the right-of-centre media market as a slower burn alternative to the Telegraph and The Spectator. Mosbacher says these titles don’t have an appetite for the 3,000 word essays found in The Critic.

He argues that the passage of the EU Withdrawal Agreement does not leave the magazine without a mission. “The whole Brexit debate illustrates an out-of-touchness among metropolitan liberals. I think it shows that a magazine like ours is needed but it’s (needed to cover) the wider issues, the cultural issues which underpin Brexit.”

The Critic will “not bang on about Westminster politics”, he promises. Neither will it have “a great deal on Brexit”.

Montgomery rails against the lobby journalists who he watched in his last job as they “huddled” at Downing Street briefings to agree a line and a time they would tweet it to the public.

He wants to publish things “not already being said”, such as Robert Thicknesse’s entertaining evisceration of big opera house directors and their mistreatment of their audiences. “The suburban crowd of dopey wedding-anniversary naifs, led to expect a jolly, indecent show sat in hollow-eyed gloom, rueing the day they were born,” Thicknesse wrote of the crowd attending the English National Opera’s Orpheus in the Underworld. Thicknesse is “the bad boy of opera criticism”, says Montgomery approvingly. “When a press release comes out of Covent Garden he is willing to say something unpleasant and insulting – most of them are just too keen to get the nice perks that come with being an opera critic.”

Such saying of the unsaid, The Critic’s editors believe, is the new title’s niche. “If you don’t have something like The Critic to say it, then who is going to say it?”

Ian Burrell's column, The News Business, is published on The Drum each Thursday. Follow Ian on Twitter @iburrell