The Reverend Hubert Brasier died in a car accident on a notoriously dangerous stretch of dual carriageway on the fast-moving A40 approach to Oxford. On his way to take evensong at the tiny Norman church of St Nicholas the Confessor, in the hamlet of Forest Hill, Mr Brasier edged his Morris Marina out of the slip road, not noticing the Range Rover speeding towards him. His daughter, Theresa, was 25 at the time. Mr Brasier had named her after a 16th-century Spanish nun who went on to become a great reformer of the Carmelite order. I wonder how long before cartoonists start depicting the new prime minister’s face superimposed on Bernini’s notorious sculptural depiction, The Ecstasy of Saint Teresa?

The parish of St Mary the Virgin in Wheatley, where Theresa May’s father was the vicar, is deep in the Anglican heartlands and a place of agreeably slow-moving traffic. A mile up the hill is the sleepy village of Cuddesdon, where generations of Anglican clergy have trained for the priesthood (me included) and which one former archbishop, Lord Runcie of Cuddesdon, has described as the nearest thing to heaven this side of death. But Mr Brasier trained at the distinctly high church college of Mirfield in Yorkshire. And, to many, that made him Father Brasier.

I know a thing or two about vicars’ daughters. I have a couple of them myself. And while there is no standard model, there is nonetheless something about growing up in a vicarage that is bound to shape the way you see the world – not least a peculiar feeling of resentment that half the community call him “father” when he is your father, not theirs. Vicarage life is conducted in a goldfish bowl.

And father is always at the beck and call of others, being called away for another evening meeting, always available at the door or on the phone. “Come on in,” I would say, as a parishioner unexpectedly called round at nine at night. “Turn the telly off, kids, it’s Mrs X.” Poor girls. I once heard a vicar’s child complain that their father had sacrificed their childhood on the altar of his principles. That stung. On Desert Island Discs, Theresa May spoke of “early memories of a father who couldn’t always be there when you wanted him to be … I have one memory, for example, of being in the kitchen and looking up the path to the back door, where a whole group, a family, had come to complain about an issue in the church and that’s it, just knock on the door and expect to see the vicar.”

This was the formative world of the new prime minister – unflashy service, community, warts and all, and personal sacrifice. The Christian faith “is part of me. It is part of who I am and therefore how I approach things”, she said. And, unlike the patchy public school religion of her predecessor, her faith feels entirely convincing to me. Among her Desert Island Discs picks were two hymns, including Therefore We, Before Him Bending. Now this really is a fascinating choice. First, because no one who wasn’t a proper churchgoer would ever have heard of it. And, second, because it betrays the enormous sacramental influence of her high church father. Benediction, the worship of the blessed sacrament – or “wafer worship” as Protestant scoffers often describe it – is pretty hardcore Anglo-Catholic stuff. That’s why she was named after a 500-year-old Catholic saint. As time goes on, this background is bound to shape her ministry – and yes, that’s how she will think of it.

Teresa of Ávila’s reforms of the Carmelite movement came as a response to the crisis of the European Reformation, to what she called “a world in flames”. They also took place as new possibilities of trade were being opened up beyond Europe, the other side of the Atlantic – her brother, fighting with the Spanish army, sent her some of the first potatoes from the New World. Theresa of Downing Street has inherited a strangely similar set of challenges and opportunities. And no doubt it won’t be long before she also recalls Saint Teresa’s prayer: “O my Lord, how true it is that those who work for you are paid in troubles.”

@giles_fraser