Di Cross from Extinction Rebellion Salisbury said this was a “major health issue”.
After an area is given bathing water status, the EA will regularly test the water and the results are made public.
Ms Cross said this meant “everybody using the water can have some idea as to whether its safe”.
She said: “This designation will force the EA to keep an eye on what is going on.”
Ms Cross said pollution also affected animals and habitat.
“Salisbury is renowned for its five rivers, the chalk streams, we have some of the rarest habitats in the world – we should be looking after them,” she added.