Most clubs and associations in the UK will have some kind of logo or emblem, whether it is simply printed on the newsletters, put on a website or used to fully brand the club and it's associated merchandising products.
The type of badge that is most suitable will depend upon the age of your club members, the club's activity and the intended purpose of the badge.
For example, if your club is a school holiday or child activity club and you want to reward participation, then a 58mm button badge saying something along the lines of "I Went Pond Dipping" or "Summer 2017 Trampolining Club" will be appropriate.
Alternatively, if your club is an adult choir and the badge is to be worn on a jacket lapel, then a clutch-back badge is more appropriate.
If you club hosts or attends more formal meetings, then a resin name badge may be more suitable.