Hi if you go on pepipo site and leave the an account of what happened usually one of the admins for want of a better term will give you some advice.
Its also worth looking at the signs in the particular car park, signs must be clear and in this case i would think point out that the car park for the health centre is not the same one for the hospital and that vehicles must be logged on the tablet in reception.
As I mentioned earlier I dont know all the inns and outs of your situation, but you indicate you had a medical emergency, parked in a disabled bay with the badge displayed and parked if this is indeed the case then I doubt the parking company would take it any further.
Also if the person you spoke to told you not to appeal the this could be in breach of the BPA (British Parking Assocation) code of conduct (I believe SABA are a member) as the parking appeal in this case would be dealt by POPLA (Parking on Private Land Appeals) and should be in theory ‘independent’ and have nothing to do with SABA.