I don't know about 50s and 60s, I do know that HMS Grenville was broken up there in the mid-80s. That ship was a 'U' class 1941 Emergency Pattern destroyer, pretty much identical to HMS Cavalier when built. HMS Grenville was converted to a fast frigate in the 1950s, so ended up looking significantly different.
The reason the ship didn't have a name beginning with 'U' was because she was built to be a Flotilla Leader and they were named after famous naval officers.
HMS Daffodil was broken up there soon after and she was a Great War Flower Class Sloop, sister ship to HMS Crysanthemum, also called HMS President. Together, the two ships made up HMS President, the Headquarters of the London Division, Royal Naval Reserve before the unit moved ashore at St Katherines Dock in the 1980s. They were moored at the Embankment.