In a previous life, prior to a job in IT, I worked for the Council Tax Office in Scotland for 11 years. I know that there are slight differences in legislation between Scotland and England but to the best of my knowledge these are more to do with means of collection (we have warrant sales here and you have court appearances.....I believe).
Anyway, with regard to 'Severe Mental Impairment' which is what AD falls under, provided the person concerned was in receipt of Disability Living Allowance any Council Tax exemption (not rebate, that is a separate thing) or 25% discount was always backdated. A rebate is income based and is not backdated (that's where the difference lies).
The 25% discount is effectively a single persons discount where there are 2 people living in the house and the second person is disregarded (this can be for a variety of reasons, including 'Severe Mental Impairment' or they are a student or whatever).
However, where a person lives alone and qualifies for exemption, provided the GP will provide a letter confirming date of diagnosis and there is proof that someone has been in receipt of Disability Living Allowance (or at that time Attendance Allowance....not sure if Attendance Allowance still exists) then exemption can be backdated.
If you're having trouble getting it backdated, involve a local councillor or MP, a letter from them will usually do the trick in conjunction with the relevant documentation.
Certainly the council I worked for didn't have to have a letter from a councillor or MP, but for other things that usually helped to sway things in the right direction.
It's worth a shot!
Mandy