I am not an AME but surely the CAA is concerned that you lose consciousness ie you become disabled, and that is it current ie it occurred at your recent medical. Although it is unlikely you will be asked to give blood whilst flying, it is possible you might cut yourself and it is unknown whether you would then lose consciousness. you might say no, but the CAA must play safe
Harsh though it is, there is logic is not granting a medical to a pilot who loses consciousness. It is the core concern of the CAA
I really think you would be better advised to deal with the underlying condition, in the same way as if you had a heart problem that causes a loss of consciousness. There are several specialists who deal with phobias and help people cope with their fear. A good example are the small number of patients who cannot undergo an operation and run out of hospital or faint on being brought into theatre. Once you can demonstrate you have had this treatment and can successfully give blood without fainting you will have a much stronger argument