"Forward, together". The title of the Conservatives' election manifesto invites comparison with Margaret Thatcher. It was before these words that the Tories' great landslider spoke at her party's 1980 conference. But it is here that the similarities largely end. For Theresa May is the first Conservative leader to truly grapple with Thatcher's legacy.

The economic forces that the former prime minister unleashed – through privatisation, deregulation and tax cuts – had ambiguous and unintended consequences. While dealing a hammer blow from which the socialist left and the trade unions never recovered, they also undermined the ordered society that she revered. The speculative frenzies of the market, the decoupling of contribution and reward and the surge in private debt contradicted her values of responsibility, fidelity and thrift. Thatcher's ideological inheritors, many of them more doctrinaire than the Iron Lady herself, adopted a dogmatic faith in capitalism at odds with traditional Tory pragmatism.

May's mission is to rehabilitate this older strain of Conservative thinking. "We do not believe in untrammelled free markets," declares a section entitled "Our Principles". "We reject the cult of selfish individualism. We abhor social division, injustice, unfairness and inequality. We see rigid dogma and ideology not just as needless but dangerous."

May's manifesto, authored by her fiercely loyal co-chief of staff Nick Timothy (along with Tory ministers George Freeman and Ben Gummer), proclaims a belief "not just in society" but "in the good that government can do". There are echoes of Beveridge ("five great challenges"), of Burke ("society is a contract between the generations") and of Blue Labour (whose founder Maurice Glasman recently met Timothy).

The ensuing policies do not seek to reverse Thatcherism (as Labour's manifesto does) but to correct it. The manifesto promises a "tarriff cap" on energy bills (which have continually risen under privatisation), "worker representation on company boards" (strengthening labour against capital), "a new generation of council housing" (neglected ever since Thatcher's Right to Buy) and a "modern industrial strategy" (legitimising the state as an economic actor).

Even in the case of Brexit, May is wrangling with another Thatcherite bequest. Despite her latter europhobia, it was the former prime minister who took the UK into the European single market, extending the free movement of goods, services, capital and people. As the EU expanded, the liberal imperative of growth clashed with the conservative imperative of order. Net migration from Europe now stands at 168,000, a level regarded by May as unsustainable. To this end, the manifesto recommits the UK to single market withdrawal (in order to limit free movement) and renews the aim of reducing net migration to "tens of thousands" a year.

Every prime minister since Thatcher has dwelt in her ideological shadow. The Brexit vote, one of the ruptures to which the UK is given roughly every 35 years (1906, 1945, 1979, 2016), constitutes a natural punctuation mark. Thatcher’s unintentionally liberal settlement could be supplanted by May’s harder-edged conservatism. Far more than David Cameron, who sought the middle way of “the big society”, she heralds the role of the state in promoting national greatness, maintaining social order and widening equality of opportunity.

Governments are frequently better judged by their actions than by their words. If, as the polls suggest, May's return to Downing Street is inevitable, the ensuing years will be defined by one task: Brexit. But the intention of her manifesto could not be clearer: to bury dogmatic Thatcherism.