It would probably depend on the individual club.
We're a long way from you - in north west Devon - and we quite often get visitors especially people who are taking a few days holiday down here, and fancy a few hours break from the wife and kids. They come along and borrow a club rifle, shoot a course or two, have a chat, and off they go.
As a matter of procedure we always ask visitors to confirm that they comply with the Firearms Act section 21 which restricts and in some cases forbids those who have had custodial sentences handling firearms.
We don't accept unexpected visitors, they have to have made contact beforehand, and they come as a guest of a member or as a club guest, signing in etc.
Our insurance doesn't require visitors to be British nationals and "foreigners" are welcome so long as there is no language issue bringing unacceptable risks.