In theory you could set up such a club range as described above. This would likely result in your local firearms licensing officer foaming at the mouth. The only action I could envisage being taken against the club would be for the police to set the Health and Safety Executive on the club. They would look to find what is acceptable as fewer and fewer people know anything about firearms so they would look to the Home Office standards and if the range did not comply then they would take action by means of prosecution and/or prohibition notices.
Another issue would be that as such a club can allow random people to shoot without needing any form of membership would be the matter of prohibited persons gaining access to firearms and ammunition, particularly if it would be possible for a shooter to sneak ammunition out of the premises. Careful management of such a club would be needed. I'd love to see a resurgence of such clubs although I suspect that the Firearms Act would be amended if they became popular.