I don't know much about flying in the USA so its hard to list differences. I assume you are familiar with the UK quadrantal rule for IFR flight off airways above 3000' (airways use the semicircular rule, with exceptions).
The main difference as far as I can see when watching USA training videos is that the UK is much more formal and accurate about reading back clearances and instructions. Publication CAP413, which I believe is now available to read on the internet,
lists the items which must be read back in full.
For an airways flight, you will rarely fly the flight planned route. Expect to suddenly get "route direct XXXXX, contact London on 123.45" where XXXXX is a reporting point you weren't planning to use and can't quickly find on the map. If this happens and you don't know the reporting point you should request track to XXXXX from present position. This gets you heading in the right direction quickly, and makes locating the new reporting point easier.
If you have any specific IFR questions I will be happy to tell you what I do, and if any of it is wrong, no doubt others will come out of the woodwork to point out my errors !