Oh man, tough decisions lay ahead of you. I would leave the huges behind for now simply because they're pretty bulky, unless you want to make room for a Snowspeeder. If you're going to be buying some Force Unleashed boosters while you're in England, you might want to bring a Snowspeeder or some Hoth stuff. I'm all about the themes...
But in terms of what to bring, I would bring enough to fill a couple of lightside and darkside squads. Make your favourite pieces your priority. I'd probably bring Rebel and Imperial figures along for the first leg. Like Rebel Storm almost, except with key pieces of your choosing. Plus some Fringe. Plus, the upcoming set will provide the most support for those factions first.
It won't be difficult to bring a couple of NR pieces too, if you want to have some variety.
I have full sets of everything that's been released as well, so if I were moving I'd have the same dilemma. I might bring some Republic Jedi as well. I know they're not the most competitive but they do have some of my favourite characters...
Are you going to be staying there a while? Are you eventually going to have the rest of your collection follow you to London?