Some people believe that Theresa May has had her day as a Tory leadership contender, but she is a woman who has been underestimated throughout her career. Furthermore, as Angela Merkel, Tessa Jowell, Margaret Hodge and Harriet Harman will tell you, we are in the day of the (slightly) older woman politician. And, while Margaret Thatcher was certainly not an advocate for more Tory women, her legacy is a Conservative party who would not find it impossible to countenance another woman in charge. Could that be May?

Throughout her political career, May has never been seen as “a rising star”. She was involved in politics at Oxford University having gained a place from her grammar school, but was not particularly pushy or sparkling future leader material. She worked in banking for a period and was a councillor in Merton. She fought two unwinnable seats before finally getting elected to parliament in 1997. So no easy, gilded rise through the party for her. Being on the receiving end of some of the misogyny found in all parties’ selection procedures may have been the spur which led her to declare the Conservatives the “nasty party” in her famous 2002 conference speech as party chair under Iain Duncan Smith’s leadership. She is a bit of an outsider, willing to argue that her party had to change and to reach out beyond its natural supporters. She is no Robert Halfon-style, blue-collar Conservative, but nor is she a “posh boy” – perhaps the perfect positioning for a future leader.

Thatcher prided herself on being an ‘honorary man’ – no feminist solidarity for her. However, May is much more comfortable supporting other women – she is an advocate of the Tory party’s efforts to find more women candidates. As party leader, she might well find ways to appeal to the older women who tend to vote, but have not always been attracted by the “calm down, dear” machismo of the current Tory leadership.

A winning party leader will have to command the political centre-ground. May is no rightwing ideologue. She shows little passion for eye-catching policy announcements and has rarely, in recent years ventured beyond her Home Office brief to express strong views or a sense of the direction she would like to take the country in. The British public may not be attracted by demagoguery, but they will need a clear idea of what a May leadership would believe in and do. This could be an even greater barrier to actually getting elected within the Conservative party to begin with. For example, May has largely avoided the issue of Europe. She did make a speech last year criticising the stifling effect of European Union regulation, but the context was interesting. Some saw this as an attempt to broaden her appeal within the party, but it was also made at the time when she was attempting to win support to opt back in to a range of EU justice and home affairs measures including the European arrest warrant, which the government had opted out of in a grandstanding gesture. She may have to make ideological gestures to win Tory support, but is fundamentally pragmatic.

However, that is not to say that she is not willing to be brave in taking on those who she feels need challenge. Her “nasty party” speech was one such example, but more recently she was willing to offer some home truths to the Police Federation at its conference. This was certainly at a time when the Fed was already weakened by internal divisions and the police was dogged by scandal. But, as any Home Secretary knows, the conference can be an unpleasant and surly event and it shows mettle to take them on in this arena.

Her time as one of the longest serving home secretaries is a double-edged sword for an aspiring Conservative leader. Being Home Secretary is a serious and difficult job – holding onto it for as long as she has means that nobody could doubt her credentials to take one more step up the ladder. Dealing with the security, cross-government issues and “events” which are the bread and butter of Home Secretaries is possibly a better qualification to be Prime Minister than the more controlled environment of the Treasury. However, the all-encompassing seriousness of the role also makes it more difficult to win support as a future leader or prime minister. Being Home Secretary with the current policy portfolio is essentially about stopping bad things from happening. It does not leave a lot of time to make the wider political arguments or to engage in the “hopey, changey’” thing which many would look for in a future leader.

She has made mistakes – alienating the civil service in a particularly cavalier shifting of the blame onto senior Border Force official Brodie Clark for supposed weaknesses in border security when the fault was in her policy decisions. She has shown bad judgement and a lack of imagination in sticking with a crude immigration cap which achieves the double whammy of being impossible to deliver and perverse in the impact of trying to.

There is no doubt that May is not a clubbable or particularly warm person so has not built up a cadre of enthusiastic supporters. She has lost some good ministers from the Home Office, like Nick Herbert and Pauline Neville-Jones, suggesting that she may not excel at building the sort of team spirit needed to win a leadership bid and maintain the ‘machine’ necessary to be a successful leader.

However, she has built her career so far on not being a “natural” for each of the political jobs she has held. She has outperformed expectations and has some of the ingredients necessary to move the Tory party on from the dilettante gentleman, amateur approach of David Cameron. It is a record and an approach which just might attract both the party and those voters who Labour so desperately needs to win back. Don’t write her off yet.

This essay is from Face-Off, a series of linked articles by Progress on the next Conservative leader.