> The Roman influence is limited mostly to place names. Otherwise Latin had basically disappeared from the island.

Recent research, namely an article by Lars Nooij & Peter Schrijver [0], suggests that a population speaking Latin/Romance may have remained present in Britain until the late first millennium. Granted, the effect of this local Latin would have been on Welsh more than English.

[0] https://doi.org/10.1515/9783110776492-004