Elements of Style is the first book everyone suggests, although I didn't find it all that useful when I got around to buying it. I'd suggest checking it out and then later getting more prescriptive books.
While I'm not sure I'd recommend it as a second or even a fourth book, I'm rather fond of the rather old fashioned (OK, it's a century old...) and most certainly not American The King's English: http://en.wikipedia.org/wiki/The_King%27s_English
There's an on-line copy of the 2nd edition linked in the above that should give you an idea of if and when you want to try it; at the very least you should try this bit right now: http://www.bartleby.com/116/101.html (well, I love it...).
My copy is this recent printing of the 3rd edition: http://www.amazon.com/Kings-English-3rd-H-Fowler/dp/B0015NYN...