Apart from the commercial
Haven sites there are hundreds of other sites to choose from, there are commercial sites, club sites and small private site.
The Haven sites seem to refer to caravans as "tourers", presumably to differentiate from static caravans.
In addition The Caravan and Motorhome Club and the Camping and Caravan Club both list their own site on their website. You don't have to be a member to use them but members do get a discount.
Caravan and Motorhome Club
Camping and Caravan Club
They also have links to small private sites which they monitor called CL and CS sites.
One search site that I find quite helpful is:
The UK Camp Site
Then there is Google, just type a town or area followed by "caravan site" and it will come up with something.