Theresa May joined the party of Ted Heath, and she never sat in Parliament alongside, still less under, either Margaret Thatcher or John Major.
Her party made her its Leader without an election precisely because she was a Remainer and a supporter of same-sex marriage, not necessarily in that order.
She has floated economic and related ideas that 18 months ago were peculiar to Jeremy Corbyn and John McDonnell, and which are still well to the left of those of most Labour MPs.
Unsurprisingly, then, there is an awkward squad in her Conservative Party.
But it is not on the Right.
The opponents of grammar schools, something that most Conservative MPs are if they think about state education at all, have entirely seen off her flirtation with those institutions.
But the Remainers turned Soft Brexiteers, if they have turned at all, are hard on her heels. In any case, they know that she is one of them.
She could yet antagonise the social liberals, who are the huge majority even if a certain number did have to vote against same-sex marriage in order to placate Constituency Associations that would no longer be of that view today.
More than any other, that tendency looked to her to spare it a Leader who believed that women without children had no stake in society.
Her parochialism has already infuriated the Arabists, who had backed her to the hilt, and whose most vocal figure she had made Deputy Foreign Secretary, in which position he is now the subject of a public death threat by Mossad's main man in London.
The Leaders of both parties could yet be removed for being insufficiently committed to the retention of freedom of movement, and for being overly tolerant of even mild social conservatism.
The only difference might be that the removal of the Labour Leader would be because he was too pro-Palestinian, while the removal of the Conservative Leader would be because she was too pro-Israeli, or at least knew too little about the subject to override those who were.
But Jeremy Corbyn is extremely unlikely to be deposed by a wildly improbable alliance of irreconcilable Blairites and ultra-Leftists who both believed in unrestricted immigration and in not giving knighthoods to long-serving backbenchers who had voted against same-sex marriage.
Whereas Theresa May looks at ever-increasing risk of being knifed.
By a combination of believers in unrestricted immigration, in not giving knighthoods to long-serving backbenchers who had voted against same-sex marriage, and in the veneration of the memory of Glubb Pasha, which would be the second time in a decade that the pro-Arab interest had brought down an excessively pro-Israeli Prime Minister of the United Kingdom.
It is contestable that any of those positions is left-wing, as such. But they are certainly not those by which the Conservative Right defines itself.