Batflu/WuFlu/Chinese Virus (because it's from China)... 
Joking aside, seeing as how all passports are chipped, why not have it added to your passport details? Obviously it's going to be an issue if you travel, so that would be sensible, or your NI number to satisfy those xenophobes who think eating a curry is foreign.
UK passports are read only, so adding additional information would require everyone to be issued a new passport every time the medical data changed.
There may be a backdoor hack into the RFID chip on the passport which may allow it to be erased and re-written, but so far no hackers have found it so if it is in there it's well hidden. If they are re-programmable then you'd likely have to return it to HMG for them to do it due to security certificate issues.
NI numbers are issued shortly before your 16th birthday. Child passports are required from birth, so NI numbers don't work for children.
The way I see this panning out is that countries will refuse you entry unless you can prove you have medical insurance covering you for a prescribed list of ailments.