Your county smallbore association is normally a good start and look at their club finder.
This is the Warwickshire SBRA site. Look for clubs that say LSR or SPORT.
Hope you find one suitable. If you don't get a reply from a club then contact the county contacts who can chase on your behalf or have up to date contact details as I know from experience clubs are useless at keeping the county up to date with latest website details etc.