Richard, I think you are getting a little confused. Car clamping on private land has been made illegal.
As it states in your most recent link:
From 1 October you can no longer have your car clamped just because you spend too long in a car park or park where you shouldn't have.
The police, DVLA and some other organisations will still be able to clamp your car, for example if you don't pay your car tax or if your car is unroadworthy.
You can still get parking tickets on private land. A two stage appeals process has been set up to deal with parking ticket disputes. This can be used by parking companies who are members of the British Parking Association.