This, plus strong if informal cultural pressure to assimilate to being English.
Remember the process of anglicization took hundreds of years. There have always been Celtic speakers in England: in Cornwall until a few hundred years ago, in villages along the border with Wales until the 20th century, and also in the cities through immigration. It looks like a Celtic language was spoken in N. England / Southern Scotland into the 12th or 13th century, well over half a millennium following the English invasion / conquest / friendly takeover / whatever you want to call it.
The Anglo-Saxons probably wouldn’t have objected to the concept of genocide, since they were a pretty ethnocentric bunch and a warrior aristocracy besides, but they also didn’t practice it. If they did, they weren’t very good at it.
As far as place-names, note that even today there are Celtic / English place-name pairs that are unrelated: Old Welsh Ty Gogofog / Nottingham, modern Abertawe / Swansea, Abergwaun / Fishguard, Caer Grawnt / Cambridge, and others that look unrecognizable because they are loan translations or distant cognates: Rhydychen / Oxford, Caer / Chester. So the lack of Celtic place-names could mean a period of bilingualism rather than replacement.