Then perhaps you should go and do what was suggested way above and go and listen to Jon Boden doing Innocent When You Dream for a start.
This is an English musician interpreting a Tom Waits composition in an entirely English style.
Or look at the work of Simon Ritchie as an obvious example (or that of any eceilidh band) to recognise how these musicians are incorporating and adapting music from what you might (but I don't) categorise as from outside the genre (simply because I don't recognise it as such) and making it their own.
This is directly opposed to just taking mainstream pap and reproducing it as identikit McMuzak in a back-to-front baseball hat.