AT LEAST among parliamentarians, there was a clear winner in the battle to become the next leader of the Conservative Party, and thus Britain’s next prime minister. In the second ballot on July 7th Theresa May, the home secretary, secured the support of no fewer than 199 of the 330 Tory MPs. Her challenger, Andrea Leadsom, the energy minister, got 84. In third place was Michael Gove, the justice secretary, with 46 votes; he now drops out.

Mrs May and Mrs Leadsom will now go forward to a postal ballot of all 150,000 or so Conservative Party members, the result of which will be made known on September 9th. On the face of it, Mrs May should win easily. Not only does she have the backing of the overwhelming majority of Tory MPs, but she is also well known in the party after serving over six years in the demanding post of home secretary. And she had a short period as party chairman.

Mrs May is not the sort of crowd-pleaser who wows party conferences; nor is she seen in Westminster as particularly warm or friendly. But she is generally respected by colleagues, party members and officials. Although socially relatively progressive, she is seen as being on the right wing of the party and she has long argued fiercely against excessive immigration. Although she argued for Remain in the June 23rd referendum on European Union membership, she did so in a decidedly low-key way.

Yet that will be her most vulnerable point in the battle against Mrs Leadsom, an ardent Brexiteer. The energy minister lacks political experience (she has never been in the cabinet) and, at least until the Brexit campaign, was relatively unknown. Even in the campaign, she ceded prominence to bigger hitters like Mr Gove and Boris Johnson, a former mayor of London. But she impressed some of those who watched her in debates and on television. And, with Mr Gove and Mr Johnson contriving to destroy each other’s chances, Mrs Leadsom now carries the pro-Brexit banner.

Her main argument to party members, a majority of whom are likely to have backed Brexit, will be that the next prime minister should be somebody who did so as well. She points to her experience as a founder of the Fresh Start group of Eurosceptic MPs as evidence of her knowledge of matters European. She has had a short stint as a junior Treasury minister. And she plays up her 25-year financial career—indeed, several critics have emerged to accuse her of embellishing its significance.

Her appeal will no doubt go down well with many pro-Brexit party members. But many MPs, including quite a few on the Brexit side, would be appalled if she won. They point to claims that Treasury officials found her difficult to work with and to her limited knowledge of how Brussels works or of other EU countries. Many feel that Mrs May, who has spent lots of time arguing with fellow European interior ministers, would be a stronger negotiator. A few even draw comparisons between Mrs May and Margaret Thatcher, who became famous for her epic European battles in the 1980s.

The winner of the race will become only Britain’s second female prime minister. Neither is likely to call an early general election; the next poll is not currently due until 2020. The tasks of implementing the Brexit vote, as well as coping with a probable recession, will be enormously challenging. Whoever is the victor, she will need to be tough and have plenty of stamina.