OP, you are not entitled to use the car park on your term and conditions simply because you are a member of the gym. You are entitled to use the car park on the operator's terms.
Normally if a simple mistake has been made the gym would cancel, but you don't say they've been approached, let alone tried to intercede.
As per DWMB2, we need the notices) (is it just one) and photos of any signs.