Theresa May speaks outside 10 Downing Street on July 13, 2016.Toby Melville / Reuters

When Theresa May officially took over as Britain’s prime minister on Wednesday, in theory she was bringing new leadership to the country at a dramatic and tumultuous time. But in another way, she doesn’t look so new. No sooner had she delivered her first remarks as prime minister than Adam Boulton of Sky News remarked that May, whose speech focused on inequality and social justice, “reminded me a bit of Margaret Thatcher: ‘Where there is discord, let us bring harmony.’”

Foes and friends alike have repeatedly invoked the Iron Lady’s memory as May has risen to the fore in the weeks following the June referendum on whether the U.K. should leave the European Union, and the political chaos and leadership vacuum that ensued.

One telling example came last week, when an unkempt, red-cheeked Ken Clarke, a Conservative politician, had a hot-mic moment with another former Tory government minister, Sir Malcolm Rifkind. At the time, May was not yet the last person standing in the race to succeed David Cameron, who resigned after having staked his career on holding the Brexit referendum, in which he campaigned for the U.K. to stay in. Clarke and Rifkind seemed to believe they were off-air when they began dissecting May’s last two remaining rivals in the leadership contest, but they were caught on live camera annihilating both Michael Gove (“we’d go to war with at least three countries at once”) and Andrea Leadsom (“so long as she understands she’s not to deliver on some of the extremely stupid things she’s been saying”), before directing their remarks to May.

“Theresa’s a bloody difficult woman, but you and I worked for Margaret Thatcher,” Clarke said, before they both dissolved into laughter. The British papers did the rest.

Suzanne Moore, a columnist for the left-leaning The Guardian, wrote that both May and Leadsom presented themselves as the second coming of Thatcher, and that both were “extremely rightwing.” Being “difficult,” though, “will be a boon in complex negotiations” concerning Brexit, Moore suggested. “Having lived through the Thatcher years I’m afraid to say that her gender was never irrelevant in the way she exercised power. No, of course these women might not be feminists but they absolutely know how to run rings around patriarchal structures.”

At the other end of the spectrum, the conservative Telegraph also invoked Thatcher to cheer the virtues of a “difficult woman”: “We have had one running the country before,” its editorial page boomed, “we need another now.” In an interview with the Evening Standard, May was asked just how many leopard-print shoes she owns before the reporter posited: “The big question is whether she is a match for Margaret Thatcher.”

“I’ve never compared myself to Margaret Thatcher,” May told the paper. “I think there can only ever be one Margaret Thatcher. I’m not someone who naturally looks to role models. I’ve always, whatever job it is I’m doing at the time, given it my best shot. I put my all into it, and try to do the best job I can.”

But it’s not yet clear whether May’s resemblance to Thatcher goes much beyond the mere fact that both are women who emerged from the Conservative Party. Thatcher, the flinty, pearl-sporting prime minister who led the U.K. from 1979 to 1990, was known domestically for championing financial deregulation and having bitter confrontations with the country’s powerful trade unions. May appears to be less of a free-market hardliner; she has called for “serious social reform” to ease inequality in Britain, and proposed changing monetary policy to help low-income earners be able to afford to buy their own home.

Abroad, Thatcher was a forceful Cold Warrior, and she launched a conflict to beat back the Argentinian invasion of the British-controlled Falkland Islands in 1982. It’s less clear what May’s foreign-policy priorities will be—she is assuming the prime ministership after more than six years as home secretary, a position that kept her focused largely on domestic security issues. But where Thatcher was stridently anti-EU, May supported the campaign for the U.K. to remain in the European Union. Nevertheless, it’s May who is now tasked with shepherding Britain’s exit from the bloc.

“Not all roads lead to Margaret Thatcher, but it’s inevitable, the Thatcher factor looms large here,” said Julie Gottlieb, a lecturer in modern history at the University of Sheffield. “Thatcher was not only the first female prime minister, but she characterized her era, she had her own ideology that was named after her. Love her or hate her, she changed this country.”

It’s still a question where May herself actually stands ideologically and how that will define her tenure, according to Richard Toye, a history professor at the University of Exeter. “She’s been talking about social mobility. Where that really fits in with the policy of the government she’s been part of is something we’re going to have to judge over a period of time.” As for the seemingly inevitable comparisons to the only other female British prime minister, Rosie Campbell, a professor in the Department of Politics at the University of London, said “May is nothing like Margaret Thatcher.” Where Thatcher opened her private life to the public, May hasn’t. Thatcher wasn’t a feminist, but May is. And May, unlike Thatcher, is progressive on some social issues. “When David Cameron was elected nobody said, ‘It’s the new John Major.’”

Another question is what May’s ascent will mean for women in British politics more generally. May’s six-plus years as home secretary represented a record tenure for anyone, male or female, in that job. But women in senior Cabinet positions remain rare. “There are still gender constraints on political careers,” said David Jarvis, director of international programs at Pembroke College at Cambridge. “It is interesting we have two female prime ministers, but only one woman that’s been foreign secretary, and there’s still never been a woman chancellor of the exchequer.”

“The line in the sand for a lot of men and for some women is women being fit to run the country’s finances or issues of defense or foreign policy,” Jarvis said. “We tend to be dismissive of those arguments, they tend to be embarrassing and old-fashioned. Here we are in 2016 and might congratulate ourselves on women prime ministers, but there are still roles that are women and roles that are men.”

And while Theresa May has been a stalwart feminist during her years as a politician—11 years ago she co-founded Women2Win, a Conservative Party movement to get more women into parliament—Thatcher infamously was not; she appointed only one woman into her Cabinet while she held the top job.

Thatcher’s larger battle, argued Jarvis, centered not on her gender but her socio-economic background, which contrasted sharply with the wealthy, aristocratic “old boys” network that dominated British politics during her time. “If you read her memoirs, it’s absolutely clear that one way in which she did feel an outsider, and it absolutely shaped her politics, was more social class than gender, that she was seen as a grocer’s daughter,” he said. “She was ambivalent about large sections of what had been considered stalwarts of conservatism, the civil service, the big public schools, even the great universities, and there’s always a sense of Margaret Thatcher that she’s been critical of them.”

The old boys club remains a force in British politics. The British press made much of outgoing Prime Minister David Cameron’s membership in the Bullingdon Club, an all-male clique at Oxford University to which fellow Conservative MP Boris Johnson and George Osborne, Cameron's chancellor of the exchequer, also belonged.

“I think that [sexist] attitudes are more entrenched than one might think; it’s not just the House of Commons, it’s boardrooms, universities as well,” said Toye of the University of Exeter. Those attitudes are not restricted to men alone, as was perhaps best showcased most recently by the other woman vying for the top job, Andrea Leadsom. The Tory minister was quoted on the front page of The Times on Saturday, arguing that being a mother made her more qualified to be the next prime minister than May, who has no children. “Genuinely I feel that being a mum means you have a very real stake in the future of our country, a tangible stake,” she said.

“Leadsom managed to really exemplify some of the horrible attitudes that really exist,” said Toye. “On the upside though, you could say, yes, she said this, but she got completely shot down in flames and her leadership bid was over within 48 hours.”

Nor is lack of gender parity a Conservative Party issue. Labour has failed to produce a single female leader in its entire history, although that may change now with the Labour MP Angela Eagle challenging the embattled Jeremy Corbyn for the role.

“The Labour Party’s culture was for many many years dominated by the trade union, and the trade union movement was for much of that period predominantly male and one where attitudes towards feminism lagged behind the lay membership of the Labour Party,” said Jarvis. “That’s not the only reason, but that’s been a major factor.”

But the best way to understand May is perhaps not through the prism of her female predecessor at all. “I suppose when we have our third female PM they might start saying, ‘Is she like Theresa May?’” Toye mused. “The interesting question will be, which male leader is she most like? Why not say she’s like Harold MacMillan insofar as she’s taking over from a leader who’s plainly failed in an important way at a time of national crisis, could be seen as a ruthless individual, and could also be seen as fundamentally a quite competent person?”

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