LONDON — Mrs Theresa May, the frontrunner to become Britain’s next Prime Minister, revealed in 2013 that she had been given a diagnosis of Type 1 diabetes, a condition that requires daily insulin injections.

Asked later how she felt about the diagnosis, she said her approach was the same as towards everything in her life: “Just get on and deal with it.”

That kind of steeliness has propelled her to centre stage in the aftermath of Britain’s vote to leave the European Union (EU) and the feuding that erupted in the Conservative Party over who would succeed Mr David Cameron, the current Prime Minister, who said he would resign by Autumn.

Conservative lawmakers began voting on Tuesday to winnow the five contenders to two, whose names will go to party members for the final say. In the first ballot, Mrs May led with 165 votes; Ms Andrea Leadsom was second with 66. Mr Liam Fox received the least votes and was eliminated, and Mr Stephen Crabb, who came fourth, exited the race, lending his support to Mrs May. Balloting is scheduled to be completed next week.

Mrs May, 59, is the country’s longest-serving Home Secretary in half a century, with a reputation for seriousness, hard work and avoiding the intrigue and treachery that has gripped her party. She is one of a growing number of women in traditionally male-dominated British politics rising to the upper echelon of leadership.

“I know I’m not a showy politician,” said Mrs May last Thursday. “I don’t tour the television studios. I don’t gossip about people over lunch. I don’t go drinking in Parliament’s bars.”

One former Parliament colleague, Mr Tim Yeo, recalled Mrs May would attend his parties, but was not the type “to attract a circle of people around her roaring with laughter”. That may be just right for the times, he said, because “her caution will stand her in good stead when there is chaos all around”. Another colleague, Mr Ken Clarke, said on Tuesday in an unguarded moment caught on camera, that “Theresa is a bloody difficult woman”, noting he had worked with another woman with a steely reputation who also confronted male-dominated politics: Margaret Thatcher.

Mrs May’s tenacity has drawn parallels not only to Mrs Thatcher, but also another methodical female politician, German Chancellor Angela Merkel, also a clergyman’s daughter.

Born in 1956, Mrs May grew up mainly in Oxfordshire, an only child who was first drawn to the Conservative Party at 12. A conscientious student (a goody two-shoes, she once told The Daily Telegraph), she never rebelled against her religious upbringing and remains a regular churchgoer. Tellingly, her sports hero was Mr Geoffrey Boycott, a solid, stubborn cricketer who specialised in playing the long game.

Like Mr Cameron and Mr Boris Johnson, the former London mayor who recently dropped out of the Conservative leadership race, she won a place at Oxford (though some years before them). But while they got there by way of Eton College and joined Oxford’s hedonistic Bullingdon Club, she attended a state secondary school and had a more sedate university career.

Politics was important to her, and she attended the famous Oxford Union debating society and joined the university’s Conservative Association. At one of the association’s gatherings, a fellow student — Benazir Bhutto, the late Pakistani prime minister — introduced her to the man she would marry, Philip May.

Mrs May has described her husband, who went on to become an investment banker, as her rock. The couple has no children. “It just didn’t happen,” she told The Daily Telegraph. “You look at families all the time, and you see there is something there that you don’t have.”

Mrs May worked in financial services, including for a time at the Bank of England, while pursuing her political ambitions. She won a seat in Parliament in 1997, representing Maidenhead, a prosperous town west of London, just as her party was entering a long spell out of power. She rose quickly through Conservative ranks and gained national attention with a jolting speech at an annual party convention, an occasion usually used to flatter party activists.

“Our base is too narrow and so, occasionally, are our sympathies,” she warned her colleagues. “You know what some people call us: The nasty party.”

When the Conservatives returned to power after the 2010 election in a coalition with the Liberal Democrats, she was promoted to Home Secretary, one of the prime jobs in government, a break that might not have happened had Mr Nick Clegg, the Liberal Democrats’ leader, demanded the post for himself. Instead, he became deputy prime minister without a departmental brief, setting Mrs May on her way.

At the Home Office, she resisted pressure from America to extradite Gary McKinnon, a Briton accused of computer hacking, citing human rights concerns. But she negotiated a treaty with Jordan that allowed Britain to extradite Abu Qatada, a radical Islamic preacher. His extradition had been obstructed by the European Court of Human Rights, which feared he might face torture in Jordan.

Mrs May also won respect by confronting a powerful interest group, the Police Federation, which represents rank-and-file officers. In a speech to the group in 2014, she listed a series of police failings, demanded change and was greeted with stony silence.

Her political Achilles’ heel is immigration, which is part of her responsibility as Home Secretary. Mr Cameron promised to reduce net migration into Britain to fewer than 100,000 people a year, but the target has repeatedly been missed. Mrs May could not curb arrivals from inside the EU, who are legally entitled to settle in Britain. But arrivals from outside the bloc, which the government can control, have also remained stubbornly high. Overall, the net figure for 2015 was more than 330,000.

When the EU referendum was called, it was touch-and-go whether she would campaign for or against membership. In the end, she supported Mr Cameron’s bid to stay in the bloc, but kept very quiet. That allows her to present herself as a unity candidate to a parliamentary party that was deeply split by the issue.

However, it also means any deal she could negotiate with the EU over Britain’s future ties to the bloc would face close scrutiny from the union’s more ideological critics. That would leave her limited room to manoeuvre on the central issue, Britain’s access to the EU’s single market of goods and services.

Mrs May sought to reassure hard-liners last week by promising there would be no attempt to remain inside the EU or to rejoin it through the back door.

“Brexit means Brexit,” she said firmly, suggesting that if it falls to her to negotiate a British withdrawal from the European Union, she will, as ever, just get on and deal with it.