Hi Fizzy,
This is a question that crops up quite regularly so I checked with a contact who is an employment specialist.
If a job that you apply for asks you to complete a medical questionnaire then you will need to answer honestly. However you can say that your diabetes is fully controlled and has no affect on your ability to work. If they ask and you say no, and they later find out that you lied, then you could be summarily dismissed and there would be little that you could do about it.
If they don't ask you then you don't need to volunteer that you have diabetes. It's perfectly reasonable to assume that if they don't ask then they are not interested and your health is not relevant to the job.
If you do tell them, then you are protected by the Disabilities Discrimination Act, which prevents them from refusing to employ you solely on the grounds of your diabetes. However the DDA is a bit of a wolf with no teeth, because if you failed to land a job that you were interviewed for, it would be impossible to prove that you didn't get it because of your diabetes (unless they actually state that in writing).
Hope that helps and good luck in the job hunt!