Babalaka,
You just have to advise BA about any condition, as mentioned in the lists, and they advise you what they require from your Doctor or Specialist.
If you have a condition that worries you, waiting until you check-in or get to the aircraft is too late. You need to contact BA prior to travel or your travel agent and they will guide you to the right people in BA, or any other airline, to talk to. I am sure that all our customer service telephone operators are very used to dealing with these enquiries.
Nicholas,
If you diverted because a passenger was critically ill, it is unlikely that all the passengers would have to disembark.
A baggage identification could be done, where cabin crew move through the aircraft asking passengers to identify their own bags and any that are unidentified could be removed but I feel that if it was an unplanned condition such as a heart attack, this would probably be unnecessary. People don't normally plan to have a heart attack or another life threatening illness and it would therefore probably be the Captain who would decide if a check was required or not.