Let me put in a good word for Stefan Knopf at the link in the last post. I shipped my KLR with Stefan this past fall, and you sure can't do any better at the price. I also stayed at his place, played with his kids, asked a lot of questions about local attractions, and took full advantage of the offered space to sort gear, change oil, etc. When I got lost on the way in, Stefan escorted me to his place personally; when I forgot to take care of various odds and ends preparatory to shipping the bike, he did them for me after I left without complaint. His freight forwarders in are alsOrlando are also good people, and highly competent at what they do.
I used Warren (Warren Motorcycles On-Line
) shipping in the other direction, and I have to say that he also gave very good service at a fair price. The program is different, however, and maybe you've looked into it already....? The website I found is horribly dated, but the 800 phone number listed there is the one I used a year and a half ago. He does roll on---roll off shipping via Lufthansa; I used New York to Munich and it cost me something like $1200 US. One advantage for me was that Warren managed to make things very flexible---my bike's engine grenaded enroute, and I was a month or more late getting to New York. Warren is physically located in Boynton Beach, Florida, wherever that is.
Seems to me you've got plenty of options from Florida to Europe, although maybe fewer to the U.K. With the money you save using Stefan Knopf you can pay him to store your bike until warm weather and still come out well ahead of most other forms of transport.
I tried to post the above information and more on the shipping page but was foiled by an apparently permanent site disability.