The supposed iron law of British politics – back when an economy dominated by Big Finance seemed to be a never-ending fountain of growth and tax revenues – used to go like this: you had to present yourself as a steady pair of hands, pro-business, competent, exuding stability, not someone to rock the hull of HMS Britain. Tony Blair, speaking of Margaret Thatcher, once described his political formula: “I always thought my job was to build on some of the things she had done rather than reverse them.”

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But whether you’re a politician of left, right or so-called “centre”, insurgency has become the iron law of our time. Labour has been robbed of that sense of insurgency by Brexit: its political fortunes depend on reclaiming it.

This new iron law began to emerge during the Scottish independence referendum, which – in hindsight – foreshadowed the tumult that later gripped the rest of the UK and much of the western world. Although the yes campaign did not triumph, it led to the SNP sweeping almost every Westminster seat and virtually destroying Labour in one of the party’s cradles. Thanks to Better Together – the miserably negative anti-independence campaign in which Labour and the Tories held hands as they warned of impending doom – the SNP could portray the two parties as an establishment cartel who needed to be swept away. Scotland was an early example of what could be called insurgency contagion. Those of us who originally made the case for Jeremy Corbyn to become Labour leader pointed to Scotland as an example of how a party positioning itself to Labour’s left had succeeded – and how anti-establishment politics could thrive.

Labour’s brand of insurgency under Corbyn was crystallised by its “for the many, not the few” election slogan. Despite protestations that its origins lay in Shelley’s 1819 poem The Masque of Anarchy, New Labour had occasionally toyed with the slogan. But Corbynism invested it with new meaning: rather than a Blairite platitude centred on expanding opportunities while cutting taxes on big business, it meant that the interests of the “many” were on a collision course with those of the “few”, whose power and wealth must be challenged and redistributed. From taxing the rich to imposing VAT on private school fees so as to fund free school meals, it was an insurgent offer. But that radical energy has been dissipated by Brexit, an issue on which Labour has a dreary, triangulating, steady-as-she-goes approach. The Brexit crisis simultaneously legitimised and undermined Corbynism: it helped cement insurgency in British politics, including among the Tories - “don’t press that big red button”, the British public were told, and yet they did - but it plays havoc with the party’s electoral coalition, and sidelines the domestic policies which are Labour’s strength.

Today’s buoyant Brexit party is the most striking manifestation of insurgency: the mass rallies bubbling with energy, echoing – from the right – the Corbyn mass rallies of the 2017 election. Another danger for Labour is that May’s successor as Tory leader could annex the anti-establishment drive, and its accompanying energy, from Nigel Farage’s new tribe. Consider how Boris Johnson spat out, “Fuck business!”, an example of the under-discussed phenomenon of how the Tories have become increasingly detached from their natural social base. Even a political formation as vacuous as Change UK gets the need for overturning the status quo, even if its relentless mantras about politics being “broken”, “old politics” and the “same old Westminster way” are as contrived as May’s “strong and stable” election pitch and a crutch to excuse not having old-fashioned extravagances such as policies and ideas.

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There are those who wish Labour to adopt a bold remain position instead; but that would mean abandoning not just radical leftism, but potentially millions of its leave voters, and its hope of forming a government.

The answer for Labour is to pick fights with unpopular vested interests, causing almighty public rows which reinforce its “many” versus “the few” insurgent appeal, and forcing its opponents to make unpopular arguments siding with elites. Why not scrap knighthoods, and make the case that they reek of nepotism and class privilege? A new honours system could be offered that excludes politicians and the supposed great and the good in favour of community heroes. What about a commitment to abolish private schools and their segregation of children by the bank balances of their parents? They could act on author Robert Verkaik’s proposal for a “slow and painless euthanasia” of private education: not just ending VAT exemption, but scrapping charitable status and relief on business rates, and perhaps imposing new taxes to make them unaffordable to run.

What about tackling the scandalous collapse of NHS dentistry? As well as reversing cuts to training and pay, action must be taken to reverse the surging numbers of practices who only take private patients: perhaps a moratorium on all private dentistry altogether. Estate agents are justifiably bogeymen for Generation Rent: why not set up a national, state-backed estate agency that works on a not-for-profit basis purely to help tenants? How about bailiffs, the villainous benefactors of a dysfunctional economy that drives families into debt? Polls show overwhelming support for at least independently regulating them and new powers could ban forcible entry.

All of these proposals aren’t just the right things to do: they would help claw back Labour’s sense of radicalism, and force its opponents to be the champions of knights, private schools, private dentistry, estate agents and bailiffs. Labour’s leading lights wistfully dream of a time when Brexit no longer dominates, and domestic issues regain their supremacy. But rather than waiting, they should pick fights now – and regain the mantle of insurgency that remains their one true path to victory.

• Owen Jones is a Guardian columnist