There are a few things to mention. You should be well over rads by Sept. Are you suffering from any fatigue, tiredness etc that would affect a part time post? Are you on any other treatment eg hormones or herceptin etc.
If not or not having any side effects then do not see that you have a health problem. You would have to explain that you had to leave previous contract because of treatment for a health issue that has now been resolved. In your application I do not think you need to mention cancer. If you have to fill in an equality questionnaire my advice would be to say you have a disability. If you get the job then you can tell them about your situation in case at a later date you need some adjustments.
They can only ask questions at interview about anything that may affect you doing the job if they ask all other candidates the same. If you have to fill in medical form that info is confidential and given what you say should not preclude you from doing this job.
Lot will depend on the type of organisation where the vacancy is. Without knowing more difficult to advise in any more detail. Hope this helps. Good luck with the application.
I've just had a mast following chemo and am waiting for rads. Had to give up my lovely new job (short term contract)when diagnosed in Oct, mainly because I couldn't face the world during chemo. Have seen ad for very very part time job, starting in Sept/Oct. Would like to apply (I think and if I'm OK) as little monster starts school then (sob!) and i think I might go slightly insane if i don't have something (other than BC!) to think about. BUT... how do I talk about BC in application form and if I get interview? I obviously have to mention it as a health problem and it was the reason I gave up working. Not sure how to handle it. Any advice appreciated as have to find energy to complete applic form this week.