London has several small rivers that feed into the Thames, but like a lot of London's geographical features, they are difficult to spot because of the wall-to-wall urbanisation. Here's one river, treated very ignominiously in a huge pipe that has been excavated all around so that everyone can see its ugly underbelly. If you were a river, how would that make you feel?
So the Wandle, that Dianne mentions is lucky: it's visible and even accessible in parts with bits of parkland, or "common" as they are called in London (=common ownership= public land) for some bits of its short journey to the Thames. Here’s a map of the river, and though it doesn’t have a scale, I’m guessing the river is about 7 miles long. Dianne mentions Beddington, near the source, to the south, while I spent my early life to the north, in Wandsworth (named of course after the mighty torrent that is The Wandle!)
Alas, the blue of the map is deceptive; by the time it got to Wandsworth, the stream looked more like a cup of black coffee left over from last night.