If success was really all about who you know, then Jennifer Arcuri might easily be a millionaire by now. The American model-turned-tech entrepreneur was a friend of Boris Johnson back when he was London’s mayor. So good a friend, apparently, that he used to visit her at her Shoreditch flat; so friendly that she reportedly managed to join a trade mission to New York led by Johnson, despite not having been officially invited on the trip.

The man whose number she stored in her mobile under “Alex the Great” (to close friends he’s Al or Alexander, not Boris, which is his middle name) lent her kudos by coming to tech summits she organised. She even reportedly used his name to approach the election campaign guru Lynton Crosby for a meeting. But most alarmingly of all, the Department for Culture, Media and Sport is currently investigating exactly how a grant of £100,000 in public money came to be awarded to her (all told, she won £126,000 in grants and sponsorship – money that for many people struggling to get a small business off the ground would be the stuff of dreams). And that’s where this story moves from the realms of gossip into far more serious questions about abuse of power and position.

If there was any kind of a personal relationship that should have been declared, any conflict of interest that should have been flagged up before cheques were written, any shady business whatsoever, then we’re all entitled to answers. Indeed, yesterday the London assembly gave Johnson two weeks to provide “details and a timeline of all contact” with Arcuri during his time as mayor.

It’s not just about what the favoured few get, but what the rest lose out on

What makes matters worse, however, is that all this is emerging just as Johnson’s government comes under fire for failing to step in and help Thomas Cook – the travel company that has collapsed with the loss of up to 21,000 jobs around the world. True, the billions Thomas Cook might have needed over coming years to stay in business entirely dwarfs the sums dished out to Arcuri’s fledgling business, and there are perfectly good reasons for ministers not to pour taxpayers’ money into a failing company. But the impression voters nonetheless get is of a prime minister who will go to the ends of the Earth to help his friends, yet is distinctly slower off the mark when ordinary people are losing their jobs.

Public sympathy is with the staff rolling down the shutters on Thomas Cook stores and reps helping stranded tourists home even though they might not get paid this month. Thomas Cook won’t be the last big company to collapse in this era of rampant technologically driven disruption coupled with deep uncertainty over Brexit, and those in other vulnerable industries will be watching anxiously to see how the government responds. Expect some extremely bitter jokes about what exactly the steel industry, or the car industry or high street retailers, have to do to get Johnson’s attention.

And even among Arcuri’s fellow tech entrepreneurs, there are likely to be awkward questions about who else might have got that grant money, that seat at the table in New York, that invaluable mayoral presence at their events if only they’d had the right connections. For that’s what people really hate about this: it’s not just about what the favoured few get, but what the rest lose out on.

Boris Johnson and the tech boss who called him 'Alex the Great' Read more

It should be said that Downing Street has denied any impropriety. Arcuri too says anything she received was as the result of her efforts as a “legitimate businesswoman”. But Johnson’s refusal to answer any of the detailed questions about all this put to him by reporters en route to this week’s United Nations summit looks very much like a stalling tactic, a bid to starve the story of oxygen. He will surely be hoping it gets lost in the enormity of everything else that is to follow Tuesday’s supreme court ruling, which could yet plunge us into an early election or a constitutional crisis. But the two are not so easily separated.

When parliament is sitting, able to ask questions or launch inquiries with legal force behind them, he will find it much harder to duck. Any threat to put parliament back into recess, or attempt to bury awkward questions about his past under all the sound and fury of a supposed “people v parliament” general election, will look as if he is avoiding scrutiny – not just over the realities of Brexit but over his personal integrity. Voters have long ago decided whether or not Johnson’s character matters to them. But this is a public matter now, involving public money, which raises fundamental questions about fairness. The public deserves answers.

• Gaby Hinsliff is a Guardian columnist