A disclaimer: as a reader, I look for books that are not only clever and well-written, but (and this may be admitting to a softheaded or sentimental weakness) I want characters who are likeable, admirable, or at least fascinating.
The main character in this book spends her time visiting an incarcerated mass murdered who happened to leave one of his victim's heads in her car. Yet she finds herself visiting the killer in prison, in an attempt to understand him. Sounds like this unusual situation could have some potential: murder, moors, and a woman of curiosity.
But I was never able to find much of a reason to like her, (or "her murderer"), and it was hard to identify with the reasons why she might go through the trouble. The book bounced around to other characters as well; they were equally difficult to sympathize with. I do wonder if this book was some sort of elaborate, elliptical English political allegory (is the murderer actually supposed to be Margaret Thatcher? Is the severed head England?)
Seriously, this book does present some difficulties for an American reader. First, there are lots of literary allusions to poets and writers most Americans wouldn't know. (Unless you read literature at Oxford, perhaps.) Second, there's lots of discussion about where people live (London neighborhoods, parts of England) that apparently means a lot, but is difficult to decode. For example, if I say a person grew up in Marin County, South Boston, the Upper East Side, or Columbine, CO, you might have a whole range of associations for that person. Similarly, Drabble uses place to hint at a whole range of social and political (and perhaps economic) differences in her characters, which may inform her intended readers, but does not translate across the pond.
This dystopian novel introduces us to a cast of unlikeable characters in unnerving situations. Some of the scenes are really ugly, including a charnal house of abandoned dogs (the best thing about our protagonist is that she eventually adopts one of the surviving dogs; the oddest thing is that she's more aggitated about calling the authorities about the perpetrator, than going one-on-one with her in a fight.) Oddly, there's some author-to-reader comments within the narrative (thinking back to English 101, I think it was Berthold Brecht who tried to keep the audience distanced from the play -- this is sort of the same thing), some evocative text that may have deep meaning, (but I couldn't help thinking of the "Emperor's New Clothes" fable, where everyone went along because they didn't want others to think them stupid), and some poisonous, rather sophisticated dialog among self-satisfied and assured people you'd prefer not to know.
This may be a very unfair reading of the book - perhaps the book would be understood in a completely different way by an English reader, or appreciated by readers who prefer a more contemporary approach to literature. But it is definitely a downer.