I understand that the Romans were unable to conquer Scotland so they build Hadrian’s Wall (which explains the survival of older cultures there). But as far as I know they occupied Wales and Cornwall, so how is it that the Celtic culture (language etc.) survived in those places?
I believe that the language was transmitted with trade rather than conquest in the roman empire. At worse one would have a translator to receive orders and communicate with Rome. But with becoming part of the empire, trade develop, and all the people engaged in the trading will start to learn the language.
For that England was not well placed. It was described as a poor land by the Romans, barely worth a conquest. So I expect Rome didn’t care enough to develop it.
It should be noted that usually when we talk about languages of the past, we’re talking about the languages of the aristocracy. In rural areas, it vary wildly depending on the history of the place and the ties they had with the nearest city. No one cared about the language they talked as long as one guy there could translate for the others. They didn’t write book either. It’s only recently in history, with the idea of nation and the school for everyone, that people started to talk the same language on all of a country. You may have heard about the literacy of a population that was very low until the 60’s or 70’s. This is actually when people all started to actually talk the same language, even in remote places.