WAV: an archaeologist once said that humans are a diasporic species. We all started in Africa and spread across the globe.

Stories and music have spread just as widely: with people on the move, and by being passed on--look at a folklore motif index if you want one illustration of this. Or, as others have pointed out, the transmission of the ballads.

England itself is an amalgam of people and languages and has been constantly changed (and culturally enriched) by incomers: celts, romans, angles, saxons, jutes, scandinavians from various areas, normans and so on--and that's a very incomplete list for the first millennium. The richness of the English language itself reflects all of these peoples' speech.
For populations and culture (including music), all is flux, always has been and will be. If you don't agree, just try subtracting all the non-Anglo-Saxon words from your own conversation and poetry.

Building walls has never worked. We are one species and that's part of why foreign stories and music can touch us enough to lead us to want to adopt them--these things belong to us all and can be shared.

In the long term national boundaries will continue to shift and cultural activities will evolve and be enriched by exchange. Building walls has never worked. Not in Berlin. Not in Cyprus. Not for the Romans. You can't pull up the drawbridge now either. Throughout history, political movements that try to enshrine a 'moment of primary acquisition' lead to violence, exclusion, racial ideology.

If you are worried that English traditional music (or better, the diversity of English regional musical cultures) won't survive without the fiat of a university syllabus, then think again. Or maybe try to be the kind of ambassador for the tradition who can make others want to learn the songs and tunes.