SINCE THE DEATH of Agatha Christie and Dorothy Sayers, the leadership of British crime writing has been in some doubt. It is so no longer. P. D. James takes over.

In a string of good books, Innocent Blood is her very best -- despite its title, which could apply to any old crime story and is inappropriate to this serious, brilliantly characterized and most distinguished book. Innocent Blood to be read primarily as a novel and only then as a story based on crime and revenge. The story is fairly complex, though plain to follow. Philippa Palfrey, adopted by Maurice and Hilda when she was 8, is a strange, handsome girl who, at the age of 18 takes advantage of the Children Act 1975 to apply for a copy of her birth certificate. She has had romantic dreams that she is the illegitimate child of an aristocrat and a servant on his estate. She learns, however, that she is the legal daughter of Martin and Mary Ducton -- the former a rapist, the latter a murderer -- a couple sentenced to life imprisonment 10 years before. John had molested a child of 12, Mary then killed her. John has died in prison, but Mary is shortly to be released on parole.

Philippa determines to seek her out. For her adoptive father, a university lecturer in sociology, and her adoptive mother, a good cook and a magistrate, she has respect but no love and thinks they have none for her. They appreciate her as a clever child and are glad when she is able to go up to Cambridge.

Though she hardly realizes it, Philippa is looking for love, both to give and to take, wherever she finds it. So, with time to spare between home and the beginning of the university term, she seeks out her real mother and finds her in a prerelease hostel, allowed out to work as a chambermaid at an hotel. She is an intelligent, self-cultivated, realistic woman, and, when Philippa offers to take her on as a flat-mate for two months, she accepts.

Philippa has told Maurice and Hilda that she would be looking for a flat, explaining her reason. As usual, they take things calmly, pointing out that it will not be easy to find reasonable accommodation in central London. "If you need to borrow money," Maurice says, "let me know. Don't go to the bank. There's no point in paying interest at the present rate." "I can manage on my own. I've got the money I saved for my European trip."

Maurice tells her that if she means to move out permanently, to give them good notice as they could probably find a use for her room. "He made it sound, thought Philippa, as if he were dismissing a recalcitrant paying guest. But that was how he had intended it to sound."

She finds a flat for her mother and herself near Praed Street, over a lock-up greengrocery. It is squalid enough, but they are able to make it better, and they settle down into a curious, undemanding relationship which as the weeks go on, begins to show signs of a faint warmth that might almost grow into love.

Meanwhile, but unknown to them, they are being slowly and remorselessly hunted down by the deranged father of the dead girl, who has sworn vengeance on the murderess. t

To tell any more of the story, with its shattering denouement, would be to spoil things for the reader. Tension is maintained till the last.

P. D. James has all the gifts of the born novelist. Her characterization of each of the major figures is in depth. Philippa is unforgettable, strange as a changeling, with her emotions dried up. She is clever, efficient and, where her foster-parents are concerned, remorseless. It is easy to see how some of the genes come through from her now quiescent mother. Maurice and Hilda are drawn brilliantly, too, conscientious foster-parents who have not the gift of inspiring affection. Philippa is obviously not their child, nor have they pretended that she was. It was they who set her fantasy about the aristocratic father: What else could they have said, they wondered, when she asked questions?

James' descriptive powers are of the highest order: she sets her scene perfectly, whether it is the comfortable academic home, or the sleazy London flat which Philippa transforms. Her prose is sharp and excellent, her wit keen. This, I repeat, is not merely a "crime story," but a novel in its own right. I hope to find it on the short list for Britain's prestigious Booker Prize when autumn comes.