I just wanted to let everyone know that you can appeal your ESA late (later than one month) if you have good reason to. I appealed late (my appeal letter was 2 months after my failed ESA application medical and my forms were not done until nearly 3 months), I wrote and explained various medical problems, investigations and operations I had been having.
I should have included that I wanted to claim ESA at assessment rate while I was undergoing appeal - if I had been a member of this site earlier - I would have known that.