Britain faces a crisis of political leadership. Neither the right nor the left of politics is capable of throwing up a figure who can bind their respective coalitions together and sustain parliamentary majorities best to navigate Brexit or Remain and their aftermath.

Faith in parliamentary democracy is plummeting; belief in strongman politics is rising; the view that there is an elite, of which the political class is a member, intent only on feathering its own nest and pursuing its own sectarian interests, is widespread.

This mood is even more dangerous than Brexit – it strikes at the legitimacy of the institutions, even the idea of democracy. The problem originated on the right but it has parallels on the left. One of the by-products of the two world wars was that they bound the classes together. The politicians, financiers, business and media leaders who rose to the top from the 1930s to the 1970s were sensitive to the toughness of the lives of ordinary men and women. They had fought alongside and had depended on them; they knew they weren’t the shirkers and societal enemies depicted by the right today. Equally, men had seen their officers fight and die alongside their pals. Whatever their weaknesses and privileges, at bottom they could be trusted.

This was crucial for the construction of the Tory one-nation tradition – in politics and business alike. Conservatives such as Harold Macmillan or Ted Heath had served in war. Instinctively, they upheld the principles of the postwar settlement, just as business leaders wanted to run honourable companies that offered pensions, recognised unions and kept their own pay in touch with that of their workers. It was what you did. The entitlements that came with leadership were matched by responsibilities. You might have political opponents and adversaries but they were never despised enemies.

Today, that has been shattered. The private equity and hedge fund barons who fund Boris Johnson along with the “fuck business” prime minister himself feel only entitlement – and no serious responsibility. They are entitled to great wealth because they are capitalist “buccaneers” who create wealth; society is lucky to have them and plays no part in the wealth-creation process that is down to them alone. Skills, infrastructure, science – they are nice to have but essentially second-order concerns.

The political task is to create a Britain fit for even more buccaneering, as free from tax and regulation as possible, especially free from the EU. A NHS hospital is a place for photo-opportunities rather than representative of an institution in whose values you believe and curate. Personally, your instinct is to go private, just as you were educated privately.

One of the breathtaking aspects of David Cameron’s memoir is his defence of austerity cast wholly in top-down terms. A more honourable and decent man than Johnson, he has nonetheless no conception of how the scale of the spending cuts he authored ripped through British society – or of the new precariousness of the British world of work. We could have done even more, he opines. I doubt that if he had fought on the Somme or across Normandy in 1944 – or had not been educated at Eton – he would have been so insouciant about the social impact.

On the left, the Blair government, elected to make over Britain’s economy and society, did not leave a sufficiently enduring trace. There is no network of loved institutions and systems embodying leftwing values impossible to dismantle because their function is so well understood. There is no system, say, of lifelong learning or public investment banks, nor a network of brilliant co-operatives, mutuals and employee-owned firms or a well-understood commitment to the EU.

Instead, there was the Iraq war, covert, all-too-easy-to-reverse spending increases and an inadequate promotion of the European cause. It genuflected too much to the new responsibility-free elite, anxious to win their endorsement.

Jeremy Corbyn, his coterie and Momentum are now the counterreaction. Yet while their commitment not to make the same mistakes is understandable and in some ways admirable, they are wildly overshooting and even more locked in their own self-defined universe beyond which everyone is an enemy.

This provides the mirror image to Johnson and his malevolent troll, Dominic Cummings. Every business leader is perforce a member of the boss class; members of the Labour party beyond their group are collaborators and traitors. Their responsibility is to a particularly narrow socialism in whose name they seek to have unchallengeable control of the Labour party.

For what purpose? To lead requires an anchored personality, a convinced sense of direction that others – beyond your allies in a political party or, indeed, in any organisation – can be persuaded to share because, at core, it is right. You should also have the capacity to reach out to build the coalitions to make it happen. Lacking such capabilities, Corbyn and his circle, notwithstanding the merits of some of their economic policies, supply the relentlessly attack-dog rightwing press with the ammunition to create impossibly negative ratings, of which the aborted attempt to unseat Tom Watson is but the latest example.

It is a tragedy. Britain will face a collapsing World Trade Organization and a disintegrating global financial and trade order – but outside the safe harbour of the EU. What it requires is a broad-based left government that will seek to remain as close as possible to the EU – better still, within it – and fundamentally reset British capitalism and society. As matters stand, that is impossible.

Perhaps great democratic leaders emerge in much more porous, less class-siloed societies than our own; where their lived experience allows them to reach out to build broad coalitions. That is neither Johnson nor Corbyn. Brexit, we are learning, is much more than a crisis in our relations with Europe. It reflects a deep-set crisis in our society. One day, there will be a leader who gets it, but after what convulsions is anybody’s guess.

• Will Hutton is an Observer columnist