On the Somerset Badminton Association website under "Senior Badminton" there is a page for senior clubs in the county and a page for opportunities for beginners/improvers to find social and coaching opportunities. You can also find some of the local clubs on FaceBook thee days too.
On the same website you will also find all the club and county opportunities for juniors under the "Junior Badminton" area.
If you cant find what you are looking for on either the SES or SBA website then send us a message through the Feedback page or post a question on the Forum page. Or you could also try the "I Play Badminton in Somerset" page on Facebook.