My british hubby and I (american) moved over to England in Feb 2010, after living in the USA for 5 years. The process for you is really very easy, very simple, and very quick, especially compared to what all hubby (yours, mine, others) have to go through in the USA for their green cards, etc.
I was pleasantly surprised how easy it all was to do. I like others stressed while I was going through it, but all for no reason.
We also brough our 2 dogs over, which also was very easy to do. It is time consuming as it is a 6 month process, but all well worth it in the end, now that I sit here typing this post and my 2 fur babies are playing beside me.. Just make sure you follow all the rules exactly. Your Vet should know all about the process or they can read up on it. Our dogs were the first our Vet had don, but they took the time to do all the reading up on the rules & regulations and took care of everything for us, walking us through it all. We flew BA and they were awesome with our dogs, as was the Animal Reception Center in London where you pick them up.
Where are you moving to over here?
Best of Luck,