Scooby
In the UK, if you hold either a Shotgun or Firearms Certificate, you are placed on the Police National Computer [PNC] even though you [may] have no 'form' at all- indeed if you have 'form' the chances of you getting a licence are somewhat slim. I found all this out recently, when I applied for, and was granted, a Firearms Cert for a .22 Rimfire
In regard to Gun Clubs the position is less clear.As I understand it, they have to 'grass you up' to the local Constabulary if you become a member.
Phone your local Police HQ Firearms Dept and ask them exactly what their policy is vis a vis members of gun clubs.If they are reluctant to disclose this then write in and ask .If they still won't, write in again [politely] citing the FOI and ask them to disclose their policy.
Regarding any problems going 'Air Side' etc regret I can't assist,