Generally you would have problems getting your own policy for various reasons. As mentioned being added onto an existing one is much, much easier and I would go with that if I were you!
Exporting should be quite easy. I have imported a couple of cars (US > UK) and while very stressful it is ultimately satisying.
I would recommend Roll-on Roll-off shipping (car driven on and off the ship by dock workers). A friend just imported a Z06 'vette by RoRo with little problems.
It is best to get an agent to handle the basic jobs at both ends - they will know for sure what paperwork you need and will handle booking with the shipping line etc too.
I used Southampton EuroTerminal both times and would recommend them as a starting point. Adrian knows his stuff - they are part of Wallenius Willhemsen Lines:
Adrian Montgomery
Southampton EuroTerminal
Dock Gate 4, Test Road
Eastern Docks
Southampton, SO14 3GG
+44 23 8038 8679
adrian.montgomery (at) 2wglobal.com
PM me if you need any more info.
Gareth
PS: Latest "empeg holder" arrived Friday (note the "non starter" sticker - the 9C1 pack is supposed to stop flat battery problems, duh!)