Hi Milo,
Your trip sounds like fun if being cold and wet is your idea of fun
Where abouts are you going to be based? I'd highly recommend visiting the New Forest if you're in the south, it's where I'm from and it's highly underrated; imagine chocolate box cottages in tiny villages, totally unique scenery and the coast a few miles away. The Peak District is great if you're in the midlands, very rugged countryside and lots of free access to large areas which is unusual in the UK. Wales is pretty good too, the coast is beautiful (possibly a bit like Big Sur in Cali) and there's also the mountains, not quite on the scale of what you have in the US but nice all the same. If you can get to the lake district I'd highly recommend that too which is more in the north and obviously there's Scotland which I'll be bikepacking round in June.
There's quite a few campsites in the more touristy areas but they're probably not quite what you're used to in the US, you might get an idea of what's available by going to
http://www.ukcampsite.co.uk/. Wild camping is difficult as all the land in the UK is owned by someone and "civilization" is never far away. You can't really camp in national parks; having said that I do it and as long as you're away from built up areas and you pitch late and leave early you should be ok. Scotland is a different matter, same rules apply but it's perfectly legal and you can even have fires if you're responsible. There's info all over the internet about it. There's also a nice website that has info about and also lots of trip reports where they wild camp 'illegally'
http://v-g.me.uk/index.htm Transporting your bike around the UK has it's difficulties and I'm not a fan of the UK rail network as it's pretty knackered (I work for a company that deals with the rail industry and I heard Siemens in Germany spent 1.5 million Euros destroying a 3 kilometer piece of track to replicate UK conditions so they could test some trains SW Trains ordered) but you can turn up out of rush hour times and stand a good chance of getting your bike on the train. If you're going cross country you'll have to book it in advance but you'll need to do that anyway as turning up on the day is very expensive (it would be cheaper and quicker for me to drive to London and park than to get the train and I only live 100 miles away).
One fantastic thing we have in the UK is the National Cycle Network. I'm still amazed people have managed to implement such an extensive network for cyclists! If I could find the people responsible I couldn't thank them enough. You can see an interactive map and loads of information about cycling in the UK here
http://www.sustrans.org.uk/ Careful though, I can spend hours planning imaginary routes all over the country!
As for panniers etc. I think it's a matter of opinion; I use 2 Carradice Super C panniers and strap the tent (a Henry Shires Tarptent that I can't recommend highly enough!) to the top of the rack but I travel pretty light by most peoples standards (in the UK at least, probably not by bikepacking.net standards though
). I'd keep as much weight off your back as possible though, any weight on your back is also weight on your bum which means numbness of varying kinds and some of those are the worst kind! Trailer would be over kill in the UK in my opinion, you're never far away from a shop (although opening times are restricted unlike the US) and forget about getting a trailer on a train. Try going for some rides before you come here and get your kit dialed as the UK is pretty pricey for most things even with the weak pound at the moment.
Obviously these are all my own opinions but hopefully they've been of some help, let me know if you need any more info. Also, if you're near Leicester then drop me a line and maybe we can go for a ride, it's definitely not somewhere you'd go out of your way to visit though
Have fun and don't forget to bring warm clothes and a rain jacket!
Matt