Cancellation due to illness

I joined the gym during January 2015. After every session I would feel terrible on not be able to even stand up. After various tests, my doctor found that I have Iron deficiency due to my body not absorbing iron. I informed the gym about this and they said that if I get a letter from my doctor, they can cancel the contract without any penalties. I handed in my doctor's letter on 26 April and was also advised that a note was made on the system. A week later and without feedback, it turns out no one knows about my letter. Also no cameras that can prove who received it! I had to get a new letter. Did so and sent it to them on 19 May. now I am told, because the letter on the date is now 19 May and I said I handed in a letter on 26 April, I will have to pay a 50% cancellation penalty!! I have a valid doctor's letter for an illness I can do nothing about and after telling me I will then not have to pay penalties, they refuse to cancel my contract without me paying 50%!