I was flying in Western USA earlier this year for the first time. I found a good book over there which is like an "idiot's guide" to USA RT. It is published by ASA and called "Say again, Please" with a sub title of "Guide to Radio Communication". Author is Bob Gardner and I think it cost me about $15. ISBN is 1-56027-428-X.
This book also covers the different classes of airspace. It must be possible to get the book over here. I think there are also some King School videotapes covering USA airspace and RT and these should be available in the UK too.
I learnt a lot by asking lots of questions of my instructor during the BFR which you will have to do before you can use your US airman's certificate anyway, (assuming you get it on the basis of another ICAO licence).