Not common, but it does happen, according to annecotal information from some who have had such experiences.
The comment made by alephzeros was, and is, unsubstantiated. It implies that all UK campsites which bill themselves as family friendly do not welcome single, or more accurately, single male guests.
That may be the case with some, but just as common are membership only sites, those that do no allow minor children, privately-owned venues with the specific rules, and the many that require advance reservations.
It varies, and on-site, walk up, rental requests can be declined.
As it's against the law to camp outside organised campsites in England (yes, it happens), campers, just as for any accommodation, book in advance and many return year after year to the same location.