Being harsh on this one I have to say that it is more in the realms of fantasy or occult than Science Fiction. There is a distinct avoidance by the author of any logical explanations for what happens. We have people swapping bodies, magical gates opening through time, magical "hooks" to bring you back, and lots of macabre cripples and characters in the sewers of London. Really the stuff of horror and occult books.
But all that said - it is a good read. The pace is blistering and you have to keep up to remember who is in which body today. The story rips around the globe like an Indiana Jones movie, with the added attraction of leaping through time.
I don't want to give too much away, but I really felt it was a bit rich to have the main character give away all his good clothes upon his entry to old London, and accept rags - thereby sealing his fate at the bottom of the food chain. Had he been robbed it would have been more plausible.
As for Horrobins "Mistakes" - a bit of explanation would have been useful. What exactly was he trying to make? Beats me!
I think Powers would have done better to put a bit more logical motive into his story, to hold it together. I liked Horrobins character, and Dog-Face Joe. The description of the "Master" could have been filled in a bit more.
As I say, a fun book - but a bit uneven in places.