Take the UAV and power packs as carry-on luggage - it's illegal to carry LiPos in the main hold and generally a bad idea to trust your craft to any sort of baggage handler no matter how well packed !
UK drone law is subtly different to the States - we aren't allowed to fly over or within 450 ft of any built-up area (towns or crowds etc), and must also stay 150 ft away from buildings, major roads, people and structures. Our 400 ft maximum height rule is AGL,and the US '400 ft extension over landmarks' doesn't apply here. Also we are not allowed to fly at any site run by National Trust or English Heritage, which unfortunately is most of the good bits, and you will run into pretty much instant problems if you try and fly anywhere near the center of London.
You can use the
NATS app to check NOTAMS, and that the area you want to fly isn't in an NFZ / controlled airspace, and
UAVforecast to get the drone-centric weather / KP index information.
It
is difficult trying to find places to fly in the UK, but some general advice would be to try and find public footpaths / bridleways near empty fields you can launch from (we have loads of those !) and out-of-town countryside areas where you have a lot more freedom.
Sorry if that sounds overly negative - I don't mean to put you off, but I figure forewarned is forearmed...
Have an excellent trip and happy flyings !