I used to swim with Portsmouth Tri at the Eastney end of Portsmouth on Tuesdays (6:30pm) and Saturdays (9am). They meet at the beach huts next along the sea front, opposite the Coffee Cup. They welcome anyone - wetsuit or non-wetsuit and triathletes or just swimmers. The 10th hole is within walking distance.
I also used to swim Monday (6:30pm), Wednesday (6:30pm) and Friday (5:30pm) with a group of people at Hayling Island. They meet near the skate park not far from the Inn on the Beach.
The group that do the river swimming are part of the OSS. Put out a request on their FB page and you should get invited to join the local group on FB and get on the email distribution list. Their swims tend to be a bit more spontaneous, but more exciting as they tend to do more unusual stuff.