'Chadwell' almost certainly means the cold spring.
It comes from Old English cald wielle and was written Chaudewell in the Middle Ages. Links with St Chad are wishful thinking, says Hidden London; the spring’s water was said never to dry up and to be good for the eyes. The heath, in Dagenham parish, was called Blackheath until the 17th century, when it became Chadwell Heath.