'On' is more commonly used, as the word 'premises' specifically refers to a building and its grounds...ie not all of it is inside. However - just as you can say 'in the garden' or 'in the car-park - so I can see no reason why you cannot say 'in these premises'.
My organisation has done an interesting thing. Rather than posting 'Smoking is Not Allowed on these premises' they have instead posted 'No Smoking is Allowed on these premises'
(Or even in your own car in the car park)
This is a positive thing, you are Allowed not to smoke, rather than the depressing you are Not Allowed, which would have been repressive and open to litigation.
On the smokefreeengland site it states signs must display the following wording,
�No smoking. It is against the law to smoke in these premises� but �these premises� may be changed to reflect the name or type of premises, �this gym� or �this shop� for example.
It seems then, in England at least the use of "on" is illegal.