I think I'd be looking at a train journey as well, rather than flying. For a start by the time you get to airport at your end an hour early, and make your way through baggage claim and try and get transport from airport near London (which are all some distance away) you have lost half a day to start with. As for accommodation, I've been a long time member of YHA, so whenever I have to stay in London, I use the St Pancras youth hostel. You do have to share a room (unless you pay a premium for it) but it is a nice enough place and fairly quiet usually, and where else can you get a bed in London for under £30? They also have a restaurant that serves fairly cheap meals. You'd then need to use the underground to get to London Bridge Hospital. Some of the other youth hostels aren't so good (I'd definitely avoid the Earls court YHA one) as they tend to be full of 20 something partygoers. The other accommodation alternative is to stay somewhere just out of London and get the train in to your appointment. As has already been said, check out the train and underground routes in advance. I also never go to London without my pocket A-Z which makes it a lot easier to find my way around.