HD: There's a 'London Transport Flying Club'; I'm looking at it and their aircraft right now!
I try to avoid going to London but if we go to Craven Cottage, we just get the train; if we're going to Arsenal or Millwall, a 'One Day Travel Card' is valid on trains and buses and is better value, especially as it also gives you a discount on 'Thames Clipper' boats between Cleo's Needle and Greenwich. We don't see any point getting an Oyster card as our visits to London are so infrequent.