Although I agree in principle especially on a public road, I must state the following to avoid "Panic on the campsite"
Sec 5 of the RTA states on a road or other public place. "Public Place" has been deemed in case law to be the broadest term, i.e implied consent to general public. So although a supermarket carpark etc are private property, there is implied consent to enter at anytime so would fall under "public place".
Most campsites have an implied consent whilst open to enter, perhaps to a barrier at the reception. If this closes at say 10pm and opens again at 7am, this would make it Private Property and the RTA would not apply.
Anywhere without implied consent would be deemed private and it would make no difference if you had keys in ignition and engine running after consuming copious amounts of Babysham & Black tower.
Most campsites would be deemed as private as there is not a implied consent for all public to enter only those who had paid the fee.
So no panic sleeping in your van on a campsite
(P.s I won't even go into the Police powers on private land especially when it's your private dwelling!)