I've always wondered about this... there seem to be quite a few jobs that require work-related travel to Europe.
I don't have any answers for you (indeed, would like to know the answer myself) but here are some thoughts:
1. I doubt contacting the Home Office will be of any use (then again, I could be surprised!) as to whether you would be allowed work in Europe. You may have more luck contacting the 'Home Office' equivalent in any countries you think you may need to work in.
2. Don't know what kind of visa you have, but if you spend *A LOT* of time overseas there could be an issue when it comes to applying for ILR, in that they are not convinced that you are "settled" in the UK (I highly doubt this would be a problem for you, just something to be aware of).
And finally...
3. Many people in the U.S. travel to Europe on work-related business, all the time, without having the right to work in the EU. Your situation doesn't really sound much different, so if they can do it, in theory so can you! The only difference I can see would possibly be that most business trips seem to usually be for about 2 weeks max, whereas you don't say how long you would need to be abroad for (maybe it would make a difference?).
Good luck!