>What's strange though is that if it was a trade language, why did it only emerge and gain traction in Britain, and not across the entire North Sea?

This is a really good question, and as far as I know it isn't one that migration-skeptical scholars have a good answer for.

You could also ask it in the other direction though. If Old English came from continental Europe, why didn't any remnant of it survive there? It can't really be that all the people who spoke Old English migrated from the continent to Britain, can it?

Early Medieval Britain is fascinating for the same reason that it can be so incredibly frustrating. There are so many mysteries.