A medical diversion won't be claimable for compensation. Reimbursement of Right to Care will be OK, meals and the like, that should be dealt with promptly. For the rebooking cost, it's probably best to check with this forum first / at the time, since there were things you could have done here. So for example if you had called BA (rather than taking to the third party ground handling agent who don't do ticketing) then you have a case under LE versus TAP, where the diversion was caused by a punch-up on board the diverted aircraft and compensation was payable. As things stand I'm not optimistic since I think it can be reasonably argued that it was extraordinary circumstances, flights can be late, and you didn't give BA a proper chance to fix things. That said, BA also have an "all reasonable measures" requirement, and on a number of points you could make an argument here. So given the relatively large sums of money involved here you could make a go at CEDR just on the off chance that (a) BA just give in due to lack of legal resources or (b) CEDR decides that BA didn't do enough to help you.