Firstly , Good luck with your move. Where in the U.K
are you moving too?
Ok I'm guessing you could get a transformer to run your gear, but I would be concerned about the transformer overheating with constant use, and cutting out! Also transformers have a tendency to buzz after a while. If its possible to do so I would sell what you can in the U.S and buy new/ secondhand gear here in the U.K
Then you don't have to worry about it.
Will have a look and see what transformers are available and post back