Over the past two weeks, a strange phenomenon began to afflict Labour MPs, left-wing think tankers and progressives of all sorts. They started to wish fervently that Theresa May would triumph in the Tory leadership election. Yes, the woman who sent vans around north London ordering immigrants who had overstayed their visas to “go home”; she who has long been the darling of the Daily Mail, which praised her lukewarm speech in favour of staying in the EU in terms it normally reserves for actresses who have lost their baby weight freakishly fast; the woman who (erroneously) claimed in 2011 that human rights laws had allowed an asylum-seeker to avoid deportation because he owned a cat.

May’s rivals for the Conservative leadership included the blustering Boris Johnson, the neocon Michael Gove (“I think with Michael as prime minister we’d go to war with at least three countries at once,” as Ken Clarke put it), the disgraced Liam Fox, the largely untested Stephen Crabb and, finally, Andrea Leadsom, the brittle Brexiteer who crumbled under scrutiny. May turned out to be the only serious candidate.

When the contest came down to the final two, she continued to pursue a quiet, calm strategy. On the night it was revealed that Andrea Leadsom had suggested that being a mother gave her the edge over May, who does not have children, her rival was on the front page of the Telegraph talking about her “positive vision” for the country and profferring a “clean campaign” pledge.

Then, at lunchtime on 11 July, Leadsom pulled out, saying a nine-week campaign would be “undesirable” and that she could not hope to govern when only 25 per cent of Tory MPs supported her. (This had the happy side effect for Conservatives of delivering a swipe at Jeremy Corbyn, who enjoys the confidence of only 20 per cent of Labour MPs.) Immediately, May rushed back to Westminster from Birmingham, where she had given the first speech of her campaign, to be acclaimed as the new party leader and thus our new prime minister.

With that coronation, the yardstick against which May must be judged has changed. No longer is she merely preferable to the British Tea Party stylings of Leadsom; she must be judged on her own record and professed opinions. As we outline below, these are mixed. Nonetheless, it appears that May intends from the start to differentiate herself from David Cameron and George Osborne’s brand of corporate, chummy, laissez-faire Toryism. In background and temperament, she is already offering something new.

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The daughter of a vicar, Theresa May attended a grammar school before studying geography at Oxford University (rather than PPE or classics, the usual favourites of aspiring Conservative politicians). She worked at the Bank of England and then, after being elected as MP for Maidenhead in 1997, she was the first of that year’s intake to reach the shadow cabinet, as shadow education and employment secretary. In July 2002, she became the first female chairman of the Conservative Party and at conference that year made her famous “nasty party” speech. A succession of shadow cabinet roles followed, at Transport; Culture, Media and Sport; and Work and Pensions. When Cameron formed a coalition government in 2010, she became home secretary – historically a poisoned chalice – and she was the longest-serving holder of that post since Rab Butler in 1962.

The first inklings that May was seriously considering running for the Tory leadership came in 2013, the year after George Osborne’s “omnishambles” Budget, in which he slashed the 50p income-tax rate and paid for it by raising taxes on grannies and pasties. Addressing the grass-roots organisation ConservativeHome, May delivered a speech that strayed widely from the Home Office brief. It also ranged freely across the political spectrum, borrowing as much from Ed Miliband as it did from David Cameron. She outlined “the three pillars of Conservatism”: freedom, security and opportunity.

When backing May’s candidacy, the right-wing papers inevitably compared her with Britain’s only previous female prime minister, Margaret Thatcher. But a better choice would be Angela Merkel, a purposefully dull technocratic workaholic who has spent 11 years as chancellor of Germany.

May seems to be offering the same pragmatic spirit, which may come as a relief after the ideological fervour of the EU referendum campaign, with its grandiose promises and divisive debates. Had she spent the summer running against Leadsom, she might have had to tack right, stressing her anti-immigration credentials. As it is, given her rival’s early departure, the only substantial statement of her political mission is her launch speech in Birmingham.

This was an astonishing statement for a Conservative to give – though perhaps not as unexpected as her speech to the Police Federation in 2014, in which she excoriated a roomful of (mostly male) officers over the investigation into the murder of Stephen Lawrence and sexist language used about women who reported domestic violence. “If anybody here questions the need for the police to change, I am here to tell you that it’s time to face up to reality,” she said.

The surprise in Birmingham this week was that she talked about Britain’s problems in a way that was reminiscent of Milibandism. Energy bills were too high (an echo of the former Labour leader’s most popular policy, to freeze bills). Bankers’ bonuses had swollen, while real wages had stagnated. Monetary policy since the economic crisis, which has relied on low interest rates and quantitative easing, helped those who own their homes, at the expense of renters.

“There is a growing divide between a more prosperous older generation and a struggling younger generation,” she added. “And there is a gaping chasm between wealthy London and the rest of the country.” There was even a passage that would not have seemed out of place in a speech by Jeremy Corbyn:

“Right now, if you’re born poor, you will die on average nine years earlier than others. If you’re black, you’re treated more harshly by the criminal justice system than if you’re white. If you’re a white, working-class boy, you’re less likely than anybody else to go to university. If you’re at a state school, you’re less likely to reach the top professions than if you’re educated privately. If you’re a woman, you still earn less than a man. If you suffer from mental health problems, there’s too often not enough help to hand. If you’re young, you’ll find it harder than ever before to own your own home.”

Are these just warm words – a social and fiscal conservative appropriating the language of social justice and equal rights? Behind the scenes, May has been a quiet champion of women in the party, co-founding the mentoring group Women2Win in 2005. Her “nasty party” speech of 2002 was a rebuke to an activist base that was socially conservative to the point of indulging racism and homophobia. Sam Gyimah, one of the party’s most prominent black and minority ethnic MPs, supported May’s candidacy because of that. “The reason the Conservative Party now has roughly a third of women MPs and a record number of BME MPs is because front-line politicians like Theresa set the party on that course,” Gyimah says.

“I backed Theresa because her politics chime with my politics – that delivering on the economy is not enough if it doesn’t work for everyone. But also her track record of standing up for real injustices even where there isn’t an electoral dividend to be had, like on modern slavery and stop-and-search and her determination to confront issues head-on, which she did with our own party when she was party chairman.”

That said, her willingness to criticise her own side should not blind us to the many ways in which Theresa May is a conventional Conservative. Much of her success recalls Bill Clinton’s despairing phone call to Tony Blair about George W Bush, then a candidate for the presidency: “One reason Bush is doing so well is because he criticised one thing on the right. He is making people think he is saving them from the right.”

"But," Clinton concluded, "It's a fraud because he actually is for them on everything else. I have to find a way to expose the fraud." He never did. The opposition will hope for better against May.

Now read the full policy audit on Theresa May