Every so often, the presentational masks acquired down the years by British conservatism slip. If only for a moment, the supposed convictions Tory politicians bang on about are reduced to mere window dressing, and what cynical old lefties tend to talk about as the venal pursuit of class interests suddenly looks like a matter of unanswerable fact. In UK terms, this might be the political meaning of the Panama Papers and David Cameron’s woefully belated admission that he did benefit from his father’s offshore activities. In a season of Tory nightmares and whatever the knock-on effect for the Labour party, the upshot is a sudden and sobering look at what the Tories might actually stand for.

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Cameron would like us to think of his politics as a hybrid of the two strands of conservatism that preceded him: the belief in hard work and self-reliance embodied by Margaret Thatcher, and the patrician, socially concerned Toryism which still has a place in some Conservatives’ hearts. The result has been what the Tories have been selling us for the last 10 years: a utopia of home ownership and endless graft, where so long as you avoid being on “welfare”, the joys of social mobility can be yours, and we are – of course – all in this together.

On a bad day, this can still look like the politics of spivvery and cruelty, but the way that Cameron’s poshness spoke vaguely of noblesse oblige and social concern was arguably central to holding the whole package together. Perhaps, in the English imagination, cut-glass vowels still suggest falling-down country houses, the reassuring smell of horses and tweedy penury. Certainly, when Cameron has had to distance himself from financial and corporate misbehaviour, his accent and disposition have proved quite useful.

But the reality, as the headlines now buzzing around the prime minister prove, is that what remains of the old landed classes has largely blurred into the moneyed elites whose habits have once again been revealed in this week’s news: rich enough to buy property in the most expensive districts of the world’s big cities, and well acquainted with the world of offshore finance. Yes, career politicians of the centre left have had their own problems with such associations, which partly explains why Hillary Clinton cannot shake off Bernie Sanders, and why the reinvented Labour party now defines itself against Tony Blair. But despite the fact that Tory links with financial sharp practice are as old as time, the right kind of story can still hurt them too.

Which brings us to the letter we now know Cameron wrote to the president of the European council in November 2013, warning him against transparency moves on offshore trusts, its neat fit with the Cameron family’s complicated finances, and the extent to which, as he now confesses, the prime minister himself benefited. Only weeks before his message to Brussels, Cameron had given a speech to the Conservative conference assuring anyone listening that “this party is on the side of working people”, and rather condescendingly identifying the latter as those who set store by “never giving up, working those extra hours, coping with those necessary cuts”.

Cameron and Osborne’s supposedly exacting approach to public finances obviously had its limits

“We build a land of opportunity,” he insisted. But in the letter, he specifically suggested to Herman Van Rompuy that offshore vehicles used for what high-end financial advisers call “inheritance planning” might best be left alone. Cameron and Osborne’s supposedly exacting approach to public finances obviously had its limits. And the prime minister clearly had a keen sense of his core constituency. As one wag put it on Twitter this week, “How fortunate for people with money in offshore trusts that the prime minister went out to bat for them.” Quite so. On top of Cameron’s problems, the role of an array of Tory donors named in the Panama Papers comes with an air of grinding familiarity. Then there are Osborne’s evasive answers to questions about whether he has benefited from offshore chicanery and other matters that are on the public record – such as the fact that in 2005, his family firm gained £6m from a complex London property deal with a firm based in the British Virgin Islands. And what of the Conservatives’ increasingly hopeless-looking candidate for London mayor?. Zac Goldsmith’s family wealth has long been held in a trust based in Switzerland, until 2010 he was registered as a non-dom, and he owns two valuable houses acquired through companies registered in the Cayman Islands. His veneer of ecological concern and vague bohemianism cannot quite distract from all this, nor from the fact that his quietly formidable Labour opponent Sadiq Khan is engaging in a modern class politics, to evidently positive effect.

Some Tories are keenly aware of this stuff. With a leadership contest looming, they advise that the party ought to think very carefully. It might cast its collective mind back to 2005 and the rash decision to spurn that council-estate alumnus David Davis. It should consider that, whatever his financial arrangements, Boris Johnson might carry too much of the whiff of metropolitan privilege, and that there might be more to be said for either the comparative ordinariness of Theresa May, or – judging from recent whispers – the up-by-his-bootstraps new work and pensions secretary Stephen Crabb. We shall see.

Over the past few weeks I have spent more time than usual in London. One of the most illuminating experiences you can have in the modern capital is to take a ride on the Docklands light railway at around 6am, when the workers who keep the City going travel to their jobs. They have come from all over the planet, and they surely believeas a matter of instinct in the gospel of hard graft, self-reliance and social mobility that you hear from most Tory politicians.

The trains take them from the edges of south and east London – Beckton, Lewisham, Deptford – to Canary Wharf, which is when the awful inequality of modern Britain hits you like a hammer. And herein lies the problem for centre-right politics all over the world. As long as it seems to speak for the people in the Docklands penthouses rather than on the trains – the skivers rather than the strivers, perhaps – its problems will extend into the distance.