I see the reasons for the question. Hope I can help or offer some suggestions but will first ask some questions back.
First, is the boat going to be in operable condition, working motor
? If so, it might make sense to launch in Miami
or Ft Lauderdale and go the rest of the way south on your on. I guess this begs the next question, why launch in the Keys? Are you planning to keep the boat there long term or use that as a launching point for other destinations? If so, I might again recommend Ft Lauderdale or Miami. Reason I'm suggesting other locations, if you are outfitting the boat, traveling back and forth from the UK it will be easier, cheaper, more resources, closer to an airport
than doing this in the Keys. Also every mile you truck the boat will cost more.
Regarding insurance, for straight liability try BoatUS over here but you might also call some UK companies, Pantaenius comes to mind.
Big question, where and how will you register the boat? If UK then you're probably OK. If you plan to register in the US then there's a whole new list of questions, options and a few pitfalls to address.