The maximum price anyone who is a reseller of energy is legally controlled OFGEM. Their guidance document:
States
" From the 1st january 2003, the maximum price at which gas or electricity maybe resold is the same price as that payed by the person who is reselling it. ("the reseller"), including any standing charges "
It goes on to say that if a reseller over charges their customer for energy they would be open to civil action to recover the excess charge.
This would apply to caravan sites, and because they are treated as commercial businesses, and thus their price per kWh will be higher than domestic supplies.
If a site wished to charge per kWh they would have to be able to meter the energy used to be able to calculate the cost of energy used. That would also put a duty on the site owner to ensure the meters used to measure the energy were calibrated to the same standard as the energy sellers equipment.
However their is another and far more common approach which circumvents the OFGEM requirement. Touring sites rather than reselling the energy by metering it, they only rent access to the sites equipement at a rate which would cover the average cost of the energy typically consumed, and amortise the cost of the systems installation.
Trying to claim your usage of energy in a touring caravan should be treated as domestic usage and price capped, won't work.