The Pool River, which flows along the eastern edge of Sydenham is a tributary of the River Ravensbourne. But if you actually go to the confluence of the two rivers, or walk along sections of the river's leading to the confluence, it's clear the River Pool is the bigger river.
General rule is that the smaller river is considered the tributary when two rivers meet, so it should be the River Pool that flows into the River Thames. The fact the River Ravensbourne grabbed the name for the stretch downstream has some implications because it has become more well known and more likely to attract grant money for works along it's length.
I'd assumed that the River Pool was always the bigger river, but looking at this map from the 1850's it does appear the Ravensbourne may have been the bigger river. But.. I also know cartographers may have decided to show the Ravensbourne was the main river by making it look wider.
So does anyone know if the River Ravensbourne was once a much wider/deeper river? Has some of it's supply been lost to our drinking supply? Knowing much of River Ravensbourne and River Pool I dont think this is the case and believe the River Pool was always the larger river, and I am going to guess the much longer River Ravensbourne was more well known which resulted in it giving it's name to the stretch of river downstream from the confluence.