Ok I know this is off topic but I feel the need to mention it.
Geekyninja (and other young cachers) just because you do not have your own car it does not restrict you from caching. I'm fortunate to have a car but due to the economy and price of petrol I often take the pushbike out caching and this doesn't restrict me at all. I live on the very edge of Northampton and transport links are basicly poo so to get anywhere takes a bit of effort. I'm originally from SE London and the number of times I hear people from within the M25 complaining they can't get anywhere is crazy ... Busses, trains and (in the case of the OP) tube trains abound and can get you the other side of the city in just an hour.
So kids, in short, stop being lazy.
Right, that's that done with, SSSI's .. as others have said, in the case of the carpark the underlying geology may be protected or there may be a rare or threatened species of plant in the car park. As for the location of the caches in question, you guys are very lucky to have the ancient woodland of epping forest on the doorstep and even more fortunate to be able to place caches in it. The simple fact that there is ancient woodland may be the reason for there being a SSSI (as pollution from cars massively affects trees). The reviewer isn't aware of why it is SSSI and shouldn't be expected to know each SSSI in their area so they fall back on their guidlines and deny the cache if it is in a SSSI, sounds fair to me.