As an Englishman happily resettled in the USA for the last 12 years, I can thoroughly recommend a stalking trip to the UK. The hunting is one of the few things I miss about my former homeland. Given the current exchange rate, it is an even better bargain than at any time in the recent past.
Finding a taxidermist is not all that hard but it might be easier if you knew where you were going to be hunting so as to pick one closest to your hunt. Even so, the UK isn't that big and unless you're in the wilds of Scotland, most places are served by next day mail for more reasonable prices than the US.
I suggest you try the Guild of Taxidermists website to find a few folks who are experts in their fields.
http://www.taxidermy.org.uk/I took a quick look around a few sites and you might be looking around 60 pounds sterling ($75) for a roe euro mount plus shipping to the US.
http://www.taxidermists.co.uk/Don't forget about all the other sport available in the UK as well; winged game, depending on the time of year such as ducks, geese, snipe (yes, its a real bird and not a scam) pheasant, grouse, partridge and others are easily available. Wild pigeon are open year round as are crows and you can, if you happen to be in the right place, shoot enough of every bird species to make your shoulder sore. Ground game like rabbits abound and you might inquire about shooting a few foxes too.
The UK truly is a sportsman's paradise and with the right paperwork, taking your own firearms really isn't that much trouble either. Good luck and go, you'll have a blast!