Short of being photographed skiing at Davos with Bono, nothing says “global elite” like trotting up the steps to your very own private plane.

So no wonder Channel 4 pounced delightedly on the revelation that Nigel Farage recently chartered a private jet to reach Strasbourg, in an interview with the man himself that swiftly went viral. Who’s the man of the people now, eh?

Which is all very amusing, but ultimately changes nothing much. It would barely matter at this stage if it turned out that pint seemingly welded to the former Ukip leader’s hand was actually made of water and food colouring, just as it has never seemed to matter to his supporters that he’s a ex-public schoolboy turned City gent and politician. He will always be an anti‑establishment hero in some eyes because Nigel Farage says things “the establishment” does not. If he just keeps on saying those things, ripping into unpopular truths that politicians who actually care about the consequences of their actions feel obliged to defend, then he and his allies will thrive as long as “establishment” remains an insult. And that’s what any remainer longing for a second referendum needs to confront head-on.

Last week I chaired a panel at an emergency conference in Westminster on prospects for a people’s vote, at which good people grappled impressively hard with the question of how to look more like the insurgents next time. There was widespread agreement when the political organiser Paul Hilder, co-founder of the social action platform Crowdpac, one speaker pointed out that remain would need its own answer to the obvious leave message of “Tell them again”, but louder. For people who only voted Leave because they wanted someone to listen for once, an invitation to show those patronising bastards they can’t ignore you could resonate just like “take back control”. So what’s the comeback?

There were plenty of sensible ideas tossed around, about rooting the campaign in local communities rather than sending celebrities on the train up from London to lecture the people of Hull and Hartlepool, and using tech entrepreneurs or music industry bosses rather than stuffy CEOs to represent the voice of business. But the difficulty second-referendum campaigners have in countering anti-establishment rage is firstly that they generally are the establishment – a fact that would be obvious no matter how many former prime ministers are locked in a cupboard next time – and secondly that there is a glaring problem for any potential cross-party campaign in agreeing on how that establishment has failed some voters in the past.

It hasn’t failed them anywhere near as badly as Farage did, obviously. Remainers were remainers precisely because they didn’t want to wake up to news that pharmacists are already running out of some drugs due to Brexit stockpiling. They voted for the status quo because they worried that promising the voters moonshine while energetically fuelling anti-immigrant hatred would not end well. And – surprise, surprise – it hasn’t.

One way or another, the arguments that led us here have to be confronted once the immediate crisis is over

But nobody loves a smartarse. And that, in a nutshell, is the problem. You’re not going to win an argument to stay in the European Union, or even anything close to it, without offering a better answer to the underlying grievances that drove the leave vote and acknowledging the past failures that have discredited conventional politicians, allowing populists their opening. The problem for a cross-party remain campaign is that both parties have fundamentally different answers to those challenges.

Partly that’s because they are talking to different people. Brexit wasn’t won only in Barnsley and Middlesbrough and Hartlepool, in the downtrodden Labour-voting towns conjured up every time this argument arises. It was won in bits of rural Buckinghamshire that are not remotely left behind, and in retirement homes on the Dorset coast, and among golf club bores in blazers who wouldn’t remotely see a problem with Nigel Farage chartering a plane to Strasbourg.

This kind of leave voter was more attracted by the romance of the argument, the sound of freedom, the thrill of the wind in their hair; having personally done rather nicely out of the conventional political orthodoxy, they rebelled against it largely for rebellion’s sake. The last Remain campaign, with all its dreary warnings about what could go wrong, will have sounded nagging and nannyish to them.

Some of them have admittedly gone a little quiet now that it looks as if Nanny might have known best. The appeals to common sense from Tory soft Brexiters arguing that not long ago they could barely have dreamed of getting this far away from Brussels, are aimed at this mildly sheepish demographic. Others might just about heed a remain campaign if it was led by Jeremy Clarkson, say. But they would double down in outrage if confronted by the argument many remainers on the left are most comfortable making, which is that working-class leavers in neglected northern towns were conned into laying wholly legitimate grievances at the wrong door.

What many in the audience of last week’s conference longed to hear from a People’s Vote campaign was a no holds barred case against Tory austerity, making clear that the hardships many are suffering have nothing to do with the EU and everything to do with choices made at home. David Lammy showed how to do it recently in a powerful parliamentary intervention, arguing people have been conned. In its party political broadcasts, Labour too has begun constructing an argument that people were right to want change but that the change they actually need is Corbynomics. It’s as hard to imagine Jeremy Corbyn joining in a campaign where he wasn’t free to make that argument as Theresa May going along with a campaign where he was.

Since the one thing May and Corbyn do agree on is that they don’t want a second referendum, it may simply never happen. (As one Labour MP who has held private discussions with Downing Street over Brexit puts it, in some ways they’re oddly similar characters; both as stubborn as they are mistrustful.) Perhaps parliament will reach around them to produce a compromise soft Brexit of its own devising.

But that still leaves room for a Ukip 2.0 movement to emerge, cynically blaming the wicked establishment’s failure to deliver on “true” Brexit for everything that goes wrong over the next decade. One way or another, the arguments that led us here have to be confronted once the immediate crisis is over. And we’re going to need better answers than calling the other guy a hypocrite, even if it’s true.

• Gaby Hinsliff is a Guardian columnist