It is a fair question: how has a politician all but unknown before the EU referendum reached the very brink of Downing Street? What are the riptides and crosscurrents that have borne Andrea Leadsom to the final round of the contest to succeed David Cameron – a candidate, who, in the words of one perplexed cabinet source, resembles “Iain Duncan Smith with more hair and less charm”?

It is extraordinary to reflect that if Leadsom is declared the victor on 9 September, she will not be obliged to call a general election until 30 March 2020. Let me be clear: I think Theresa May will win, carried across the finishing line by her record, by whatever reserves of common sense are left in the Tory tank, and by the party’s collective yearning to hold on to power after 2020. Already, what the home secretary has said in this campaign illustrates that stability is not the same as continuity. We can expect more from her than Cameron with XX chromosomes.

Yet May’s own campaign team has drawn the wise conclusion from the helter-skelter drama of the past few weeks that, as one of them put it to me, “anything can happen in politics”. There is a risk – not a probability, but a palpable danger all the same – that Leadsom, having defied the odds so far, will continue to do so, and be summoned to the Palace to be appointed Britain’s second woman prime minister.

In the disjointed, ironic politics of our time, her obscurity has been her greatest asset. While the Tory boys were re-enacting the final scenes of Hamlet with poisoned swords, treachery real and imagined and terrible vengeance, she stayed behind the arras, awaiting her moment. Once Boris Johnson, Michael Gove and Liam Fox had been dispatched, she was the last Brexiteer standing – a triumph of inaction and insignificance over stardom and sensation.

Her appeal is narrow but intense, and meshes with two specific aspects of contemporary Toryism. First, she presents herself as a tribune of the people, uncontaminated by the wicked Blairite-Cameroon establishment. Her disciples see the furore over her CV – which can charitably be described as “embellished” – only as evidence that this ill-defined oligarchy is out to get her.

The notion that a sinister liberal elite is running the show in its own interests rather than those of the public is not, of course, confined to the right. It has its mirror image on the left in Corbynism and Momentum. No less than the beleaguered Labour leader, Leadsom postures as the voice of those who are ill-served by the orthodoxies of globalisation.

Yet her emphasis is cultural rather than economic – and this is the second core element of her pitch to the Tory selectorate. In Leadsomland, Brexit is only the start of a reactionary crusade. She aspires to lead a Conservative insurgency against the pulverising forces of modernity and what she clearly regards as the excesses of social diversity and contemporary pluralism.

The dilemma facing Leadsom is that the Tory membership’s social perspectives are not those of the majority

Consider what she has said so far. She is all for civil partnerships between same-sex couples – but “marriage in the biblical sense is very clearly, from the many, many Christians who wrote to me on this subject – in their opinion – can only be between a man and a woman”.

Since this is not a theocracy, I am not quite sure why such doctrine is relevant to the reform of a civil institution. What is true is that a great many Tory members did not like that reform one bit, and place it high on the charge-sheet against Cameron. They would also like to have seen their supposedly rural prime minister reverse the ban on hunting with dogs (in the 2015 election campaign, he promised a free vote). Accordingly, Leadsom has declared that “I would absolutely commit to holding a vote to repeal [it].” Leave aside for a moment the 700 hours that parliament devoted to the law prohibiting this practice: is it not absurd even to countenance such a vote at a time when the nation’s very future is at stake, and the precise form of its departure from the EU is under discussion?

The answer is that for many Tory activists such attention is entirely proportionate and long overdue. Remember: most members of this party, as of most right-of-centre parties in the west, are social conservatives before they are fiscal ideologues, or champions of public service reform, or neocon ideologues. One is reminded of Charles Ryder in Brideshead Revisited railing against the “Age of Hooper”, a bourgeois junior officer who epitomises all that he despises: the era of “the travelling salesman, with his polygonal pince-nez, his fat wet hand-shake, his grinning dentures”.

Today’s Tory activists (or at least a good many of them) lament what England is becoming, its diversity, its hectic speed, the lack of courtesy with which technology is turning their world upside down. Above all else, Tories like institutions: the regiment and the church have declined as points of loyalty but parliament and the nuclear family retain their allure and their importance.

This is why Leadsom reacted so swiftly to Saturday’s Times interview, and the prominence the newspaper quite reasonably gave to her claim that “being a mum means you have a very real stake in the future of our country”. Having claimed that she was not contrasting her own motherhood with May’s childlessness – “I don’t want this to be ‘Andrea’s got children, Theresa hasn’t’” – she proceeded to do precisely that. Her opponent, she said, “possibly has nieces, nephews, lots of people. But I have children who are going to have children who will directly be a part of what happens next.”

If you think such a low blow would never work, think again. In the 2001 leadership contest, Norman Tebbit described Duncan Smith as “a remarkably normal family man with children” – a perfectly innocent statement of fact, Tebbit insisted.

But in the context of a tight race it was perceived as an implicit dig at Michael Portillo, whose wife, Carolyn, was unable to have children after treatment for cancer. Duncan Smith went on to win the leadership, defeating the much more experienced frontrunner, Ken Clarke.

The dilemma facing Leadsom is that the Tory membership’s social perspectives are not those of the majority. Ours is a predominantly urban, diverse and culturally eclectic society. The nation may have voted for Brexit, but there is no broader yearning for the clock to be turned back: for hunting to be made legal once more, for gay couples to be denied the equality they have so recently gained, for the childless to be treated as failures. If anything, the next Conservative leader needs to do more to detoxify the party, to persuade the voters that it is more than a club for the affluent, the greedy and the reactionary.

This is why Leadsom had to deny the Times story so aggressively. Her strategy for winning the Tory leadership could easily lose the party the next general election. I think she knows it.

Do her fellow Tories? For all their foibles and eccentricities, Conservatives hate to lose. If they choose Leadsom, they will richly deserve to do so.