Nearly 30 years after Margaret Thatcher left Downing Street, and 40 years after she first became prime minister, British politics continues to dwell in her shadow. As the first female PM, and the longest-serving incumbent of the 20th century, Thatcher’s historic legacy was assured enough. But it is through her ideological afterlife that she looms largest, as a 10ft-high marble statue, to be erected in her hometown of Grantham, will soon literally ensure. For different reasons, both left and right continue to wrestle with Thatcherism’s consequences.

Every Conservative leader since Thatcher has suffered, to different degrees, from an inferiority complex. She was, after all, the last Tory prime minister to win a comfortable parliamentary majority (of 102 seats in 1987). Theresa May, David Cameron and John Major have all been forced, for significant stretches, to govern without one.

Nor has any Conservative leader been able to bury Thatcher’s legacy of free-market economics and Europhobic nationalism. Though May flirted with interventionist, statist rhetoric in the early stages of her premiership, this was never translated into a political project that challenged Thatcher’s trinity of privatisation, deregulation and financialisation.

In the sphere of Europe, every Tory leader has felt compelled to emulate Thatcher’s “handbagging” of Brussels. Major, assailed by Eurosceptic “bastards”, negotiated opt-outs from the euro and the Social Chapter. Cameron withdrew the Conservatives from the mainstream European People’s Party, aligning them with far-right nationalists, and staged a futile renegotiation with EU followed by a calamitous referendum. May has periodically issued crude threats to Brussels and embraced withdrawal from the single market – a project that Thatcher initially championed as prime minister) The legacy of Thatcherism was to transform the Conservatives from the party of entry into Europe into the party of exit; from the party of pragmatism in economic policy into that of dogmatism.

But it is not merely the right that is defined by Thatcher’s legacy. The left aspires to reverse her economic policies by, ironically, deploying many of her methods. Thatcher’s totemic Right to Buy, which gave voters a stake in her project by allowing them to acquire their council homes, is invoked by supporters of Labour’s worker ownership funds (which would require companies with more than 250 employees to transfer 1 per cent of equity annually into the company’s fund, up to 10 per cent of the total).

At last year’s World Transformed conference, Grace Blakeley, the New Statesman’s economics commentator, argued that, “Labour should think about the banks the way Thatcher thought about the unions ... You can’t build a new economy if the power relations that sustained the old one still exist.”

To suggest, as some do, that the Corbynites merely aspire to reverse Thatcherism – and return the UK to the post-war Keynesian era – is incorrect. Rather, like the new right before them, the new left aspire to establish an entirely new hegemony – a level of ideological domination that extends beyond electoral cycles and allows leaders to govern from the grave, as Thatcher and Clement Attlee do. Though key pillars of Thatcherism would be dismantled – with the privatised utilities renationalised, trade unions re-empowered and tax rates raised on high earners and corporations – the left through what I’ve called “Corbynism 2.0” is striking out in new directions, such as universal basic income, a four-day week, worker ownership funds.

The Thatcherites unambiguously confronted their foes: Tory “wets”, the Soviet Union, the IRA and the trade unions. Corbyn similarly draws strength from his opponents: New Labour, the American empire, the City of London and the right-wing press. The early Thatcherites were aided by a supportive ecosystem of think tanks (the Centre for Policy Studies, the Institute of Economic Affairs) and libertarian economists (Friedrich Hayek, Milton Friedman). Though Corbynism does not yet have a comparable intellectual infrastructure, it is similarly sustained by extra-parliamentary networks: left-wing trade unions (principally Unite), digital media outlets (such as Novara Media) and sympathetic economists (Paul Krugman, Mariana Mazzucato, Ann Pettifor, Simon Wren-Lewis).

But as it grapples with Brexit – a profound challenge for the opposition as well as the government – does Labour truly possess a counter-hegemonic project? This is the question that haunts Corbynites.

The banal debate over how the UK should recognise Thatcher’s legacy – where and whether statues should exist – is less pertinent than the question confronting the Conservatives and Labour: will any future prime minister ever again loom over this land as she does?