There is no requirement to tell your employer about your condition in the UK unless it affects your ability to do your job i.e. you may put yourself or others at risk. When applying for a job the employer may not ask you about disabilities but it makes sense to declare if if you are at risk so if you apply for a job as a bus driver or brick layer think carefully.
That said I have told all my employers about my condition and they have been very supportive along with all my colleagues. I feel so great as they ask me about it and want to know how they can help me. I am treated the same as anyone else so I can't ask more!
The short answer is that employers cannot ask you about any disabilities, unless it relates to you being able to perform the functions of your job.
As you can see, the answer really varies based upon personal circumstances and the job culture.
I never told my employers about my condition. They would find out after some time. I had employers that supported me for 6 or 7 years. And I had employers that only kept me for 2 or three years. Though they could not legally fire me for my disability they gave reasons ranging from personal incompetence to corporate down-sizing.
We never share your personal information with anyone.