I had an elective section with my second, it was at St Thomas's so I can't comment on the specific hospital stuff but had a few thoughts that might be helpful in light of your questions.
1) if all goes smoothly there's no reason you shouldn't be able to breastfeed and do skin on skin. The longest delay is actually more likely to be you being sewn up rather than whisking the baby away. In our case, he was weighed etc and then handed to my partner for skin on skin while they sorted me out. I was then in a position to try to feed about half an hour post birth. I was really worried about the logistics of feeding post section but your top half will be v mobile so in that sense no different from a VB. The main difference for me was that I did need someone to hand me the baby each time so that may be something to think about overnight (either if someone can stay with you, or be v assertive with the overnight midwives!).
Some people also say that it can take a bit longer for the milk to come in with a section. This was not my experience, but you might just need to play that by ear. I don't think it tends to be a problem, just a day or so later.
2) Hospital bag - apart from all the normal stuff, lots of very big pants!
3) If you don't get sent home with laxatives, buy some. Do NOT wait until you need them!
Hopefully someone will be along soon with some Kings specific words of wisdom. Personally I had a really positive c section experience having had a not so positive first (vaginal) birth. There are a lot of advantages, like not being completely exhausted while trying to learn to feed, look after, get to know your baby. Please feel free to pm or respond on this thread if you have any more questions.
Good luck! Xx