Re: I have a couple with them
I'll second that recommendation - I've been with Mythic Beasts for nearly 10 years and they've been consistently good. They're not the cheapest, but support and customer service is excellent.
Fonant's advice on transfer is spot-on - the only difficult bit will be getting 123-Reg to change the IPS Tag. I've seen people wait for over a week for this to happen - it should be an almost instant process, other than some sanity-checking to make sure that you're not someone else trying to snaffle the domain.