Thank yo for your post, which has recieved some great answers. I don't know if you are aware, but th UK government announced a loosening of restrictions on disabled driving badges (the blue badge) recently and it is going to include people with hidden disabilities. It seems to me that this is exactly what you are asking for. It is the Social Services Departments who deal with the practicalities of authorising badges so, if yhou can present a good enough case for recieving the badge, then they should agree under the new rules. I would advise that you prepare yourself for also making an appeal ( or three) because from my experience, Local Government authorities have an institutionalised habit of turning people down for most things on the first occsaion they ask. I believe this is because the vast majority of people just leave it at that and think they will never get what they are asking for. Statistics show that people who appeal are much more likely to get things and people who appeal thorugh a third-party ( such as a solicitor or even an informed, articulate friend) are even more likely to get whatever it is they are applying for. Perseverance and persistance seem to be the passwords for dealing with these organisations.
PS: They Offered me a badge years ago, without my even asking - but I declined because I felt I didn't need one! They did however, write me a letter stating that my bicycle was used as a walking aid and should be treated in the same way as a wheelchair. This was what I needed to present to people who were likely to stop me cycling into the toilets. I do like to have things that more precisely meet my needs!