Your first starting point should be to contact Sainsburys, explaining that the driver was a genuine customer, and perhaps appealing to their better nature regarding the bereavement - whilst the parking company don't have any better nature, the supermarket might.
If you don't have any luck with them, then ECP charges can still be beaten, but it can be a somewhat protracted process - basically you appeal first to ECP and then to POPLA. If both of those are unsuccessful, you then wait for them to initiate court proceedings. ECP usually use DCB Legal who, if you defend the case, nearly always discontinue before the hearing.
