There are a lot of scouting campsites in the UK, some that list quite reasonable rates for an overnight stay while backpacking or cycle touring. However, are these only available to large groups, scouting affiliates or can just anyone make a booking?
Scouting campsites can be run by local groups or by bigger regions or national scouting organizations or by commercial camp sites.
There are no national or international rules whether campsites not used by groups can be made available to individual guests.
In the UK (and many other countries) there are rules about whom is allowed to work or even be with children. If you do not have the right paperwork for that you will/should not be allowed to stay on a scouting site when there are children or young people on site.
Scouting sites without groups visiting are mostly closed (and locked).
But you can try contacting the owner/manager in advance. Walk-ins are very unlikely.
I have been active as a scout leader in the Netherlands and I am friends with a lot of people involved with Scouting in the UK.
I have seen people who after a group using a campsite were allowed to stay a bit longer, but only after having met the manager of the site while there with the group. There were no young people on that site at the time.
It is possible at times but it is very unlikely.