I hate to say this but you are actually breaking the law. Luckily the Police aren't too up on firearms law so the "we have an arrangement with the police" bit hopefully means you'll get away with it. Not sure about insurance if there was an accident.
Only shotgun and air rifles allow "day membership" where joe public can shoot on the same day as they first visit. Guest days are only for people known to an existing member or members of a club such as the scouts or WI.
Even the national shooting week website had this when you went to look for details about target shooting it said
The NRA also confirmed this. They said that the NRA are the only people who can have true open daysMany thanks for showing interest in this type of shooting event. Due to current legislation members of the public cannot currently walk in off the street and participate without undergoing a strict vetting procedure and police checks. However, this Event Organiser is keen to promote the club and so will perhaps be holding an introductory day to talk about the various sporting disciplines or running a guest day for members of a recognised organisation such as the Women's Institute or the Scouts. For more information about the club and its involvement in National Shooting Week, please get in touch with the event organiser – their contact details will be in the results of your ‘Find an event near you’ search.
But like I said, luckily most clubs get away with it.