In reality a lot of the mixed fishing clubs will be found in the Medway basin. There are a few very good ones and my personal opinion and comments from some tackle shop owners would say:
Kingfishers
Bromley and District
Edenbridge
I can't really comment on the more NE clubs like Maidstone victory and I have previosuly been a member of Tonbridge. I am now a member at Edenbridge, which is full but do not operate a waiting list, just first come first served in the new season. I thinks Kingfishers and B&DAS operate a members introduction only process, but a polite call or letter to the secretary should do it.
I'll sell Edenbridge to you though. It has small stream/river fishing on the Eden and the Medway. A fantastic match lake, a carp lake, access to two reservoirs and further river fishing on the Rother. Plus numerous small ponds and a beautiful estate lake. Most of the waters are pretty close to Edenbridge. Their match scene is not large but is very varied and uses a few rivers and lakes. The club has fishing at some really beautiful locations, three castles for example and coincidentally every fishery has a cracking pub a couple of minutes away .... but that's Kent for you.
If you are looking for something immediate and pretty intimate try Penshurst. They have beautiful fishing at Penshurst place and on the river Eden.
