I thought this may be of interest to share...
This morning I left my car on an unrestricted street and attempted to find the parking location at Barnet hospital. I walked to the area that looked familiar and took some pictures (added to imgur).
At the entrance the only Staff Parking sign is when turning left. There is no sign when you turn right, however the row on the right side has a sign and the row on the left has none. I believe this is where I was parked (see the spaces between the dark coloured vehicles). This area is drive-through and connects to the next set of parking spaces.
I was pretty sure ParkingEye would reject the "no signage" argument or even add the sign if they see the pictures, but...surprise, surprise...
... when I got home, I found an email response from Royal Free Parking Team saying that they cancelled the charge as a goodwill and ParkingEye will confirm this to me in the next few days.
I only wrote to them yesterday and I can't believe they actually read mails and employ sensible staff!
Happy end (if ParkingEye can't overturn this decision).
Thanks everyone.