I don't think it even requires any new legislation.
The police have been able to do you for various motoring offences on "private" land for a long time, as long as the "public" have unrestricted access to it at that time, a car park with no barrier is "public" for the purposes of a number of offences, but the moment you put a barrier down it may not be (so a locked up car park isn't, but the same one with the gate locked open for the day is).
All it require is a change in guidance.
However I suspect it won't be used unless there is either an incident (IE an accident) or they're already charging the person with other offences and want to make an example.