Sorry to hear about your condition. Painful back problems must be some of the worst illnesses to have to live with.

I appreciate that your reasons are totally genuine but I’m afraid that such is the way of British society nowadays that if you could “get a note from your doctor” to allow free business class upgrades then BA would never be able to sell another revenue CW ticket again! I think the stark reality is that if you can’t fly other than with the use of a flat bed then you need to buy a ticket that allows the use of a flat bed, or not fly.

I think it is very fair of BA to offer free allocation of a bulkhead seat under the circumstances, which would otherwise attract a fee. My observation has been that BA staff are extremely accommodating of passengers who are physically impaired (e.g. in crutches after an accident), occasionally extending to on-board upgrades, but I don’t think that would ever translate to a guaranteed flat bed, even with a medical note.