Downriver from Albert Bridge is Chelsea Bridge. Finished in 1937, it's a suspension bridge that looks like a giant metalwork project. Slightly surprising is that the main pillars are not joined horizontally with crossbars, which looks a bit modern, and you wonder how they don't fall down sideways (like that Second Severn Crossing, which we hate because it has no bike path).
From here on the north bank it's a half-assed shared-use cycle path that fizzles out when the going gets difficult and turns into a fast dual carriageway. On the south bank you have to cut away from the riverside. You skirt round Battersea Dogs and Cats Home, a refuge for lost apostrophes, and the upturned coffee table of Battersea Power Station. After that there there's top-class entertainment in the shape of one of Britain's funniest - that is, worst - cycle paths, detailed in a previous post. Either way, Vauxhall Bridge is about a mile from Chelsea Bridge.