Well then the only other one I can think of that runs through Wandsworth and the surrounding areas is the Beverley Brook.
Having lived round that area for many years there are no other rivers which meander through that area . So Beverely might be worth researching .
There are "lost " rivers the Beverley being one of them .
Thanks Shaneystar2. Sorry to be so long, but AB has been playing up. The full question (which I should have quoted earlier) is "The town of Midhurst in West Sussex; the village of Bodiam in East Sussex; the London borough of Wandsworth; and the city of Chesterfield in Derbyshire all stand, or are near, a river with the same name, although they are four different rivers. What is that one same river name?" So you see my dilemma.
Aha I see ! How about the Rother or Graveney . I can't think of anything else round there .Could be another one of these "lost rivers " .Several of them round that area .Good Luck anyway .
I've settled for Rother as it fits all of the others and now you've confirmed it for me. Thanks again. AB still playing up or perhaps it's my internet connection, like me it's getting past it.