I was lucky in having my ESA decision overturned at reconsideration. I didn't have a letter from my GP but I did send in several letters from friends and Mr Hurty (one friend works as a carer and the other has worked as both ultrasonographer and OT assistant).
Nothing on this board constitutes legal advice - always consult a professional about specific problems
Can I ask if you filled your esa form to capacity in the space boxes or did you keep it brief and straight to the point, and fill the page 18 in more detail.
I used as much space in the boxes as I felt I needed. Some of the boxes had a lot of information and some, that did not relate to my problem, were empty.
Nothing on this board constitutes legal advice - always consult a professional about specific problems