Dudley Council does not have control over the operation of private car parks. It is the responsibility of the operator to ensure they comply with requirement such as Health and Safety, as well as for setting their own prices.
The Health & Safety Executive are responsible for private car parks, i.e. where the Council is NOT the enforcement authority for the premises.
If a private car park is attached to a retail outlet, then the Council will deal with it as it enforce Health & Safety issues as a whole within the retail business.
Owners of private land, whether it is a private car park belonging to a store, or any piece of private land, can clamp and remove a vehicle as long as they have displayed a sign advising that they do operate clamping and removal. The sign should also display a telephone number to ring to have the clamp removed. This will usually incur a fee.
The onus is on the driver of a vehicle to check the restrictions of where they are parked and adhere to those restrictions. If, for example, a store advertises that a vehicle can park for up to 2 hours, they are within their rights to have the vehicle clamped if it is left in excess of that period.