I work in education and we would be crucified if we sought medical information before issuing an offer of employment. We can't even ask on the application form how many days you had off in the previous year.
We do have an equal opportunities form. On that, you can declare if you consider yourself to have a disability. Members of the interview panel are not supposed to see that information. So this is the first problem - how confidential is the information on an equal pops form in any given organisation?
The second problem is establishing continuity of employment. In education, we need to track your employment record since you left school. It's needed for child protection reasons. So, at interview, I would really quiz you on why you had been out of work, what you had done to find work etc. I think in that context it would be difficult to hide your medical history. So I would want you to reassure me as best you could that I wasn't taking on someone who was going to be an attendance problem. However, I would expect you to drive that conversation as I might be on dodgy legal grounds if I quizzed you. Remember, seemingly healthy people with perfect attendance records can suddenly find they have cancer. I hadn't had a day off in 11 years and then discover I have prostate cancer. An enlightened employer would understand that none of us know what the future holds. I have employed seemingly reliable people who turned out to be the employees from hell. I also employed someone who had had cancer and she was a total asset to our organisation. The other thing is, if I as a potential employer know you have had cancer, I will be very careful if I don't offer you the job to have very good reasons why you're not being offered the job in case you accuse me of discrimination. That's sadly a reflection of the times in which we live.
Thirdly, what about references. I've had references from well-meaning referees stating things like, 'Bob is an inspiration. His brave fight against cancer demonstrates his resilience and determination and I am sure he will be an asset to your organisation.'
Once I have offered someone a job, they then fill in a medical form. If there is something on the medical form that causes me to think that a person isn't fit for the job, I can refer them for an independent assessment of capability. I as the employer am more likely to be told that I have to make reasonable adjustments - it is possible for the independent assessor to state that the job offer should be withdrawn but I've never actually seen this happen.
Of course, I work for the government and we stick to the rules. Smaller employers may not even fully understand employment law.
If I were you, I'd contact Macmillan or the Citizens Advice Bureau for advice.