I managed to royally screw my ankle yesterday at work, and was reluctant to go along to A&E because I assumed the hospitals would still be up to their ears in problems from the bombings (OK, possibly not the most sensible of assumptions, but I was in mild shock ;)
However, we went to UCL, and their A&E at least seems to be very calm and quiet, and well-staffed - so if anyone else is injuring themselves in non-emergency ways and is worried about making a fuss - don't be daft, they do seem to be coping fine.
It's possibly also worth making sure that if you're going by taxi that the taxi driver drops you off at the NEW entrance - the old one is no longer in use, and is round the other side of the block, which is a long way if you've crippled yourself!