Will a University less likely/ not accept me if I have depression?

I just want to know if a University like Cambridge, Oxford, University of Birmingham less likely accept me if I have depression and that it affected my GCSE grades a lot?

It shouldn't affect their decision at all. If you're worried, just don't declare it on UCAS. It's not compulsory info and it's not really the unis' business

But my GCSE grades are so so bad and I want them to know that there is a reason to why they are bad and I don't want them to assume that it's because I didn't care about my GCSE's. What makes it worse is that I am going to study medicine in uni, which is competitive.
But right now I am re-taking GCSE's so that I could hopefully achieve A*'s rather than D's (and below) and I'm doing much better with my studying than the last two years even though I still have depression...
...So it's complicated if I should mention it in my UCAS form or I shouldn't :'

You have extenuating circumstances; you simply have to let your referee know so they can put this in your reference, therefore you still don't have to put 'depression/anxiety' on UCAS form but the unis still know your situation from a third party If you're re-sitting, then it's good that you're working hard to give yourself another chance