I thought no one knew who wrote Greensleeves?
But the notion that Henry wrote Greensleeves is fairly widespread. From wikipedia:
"Greensleeves" is a traditional English folk song and tune, basically a round of the form called a romanesca.
A widely-believed (but completely unproven) legend is that it was composed by King Henry VIII of England (1491-1547) for his lover and future queen consort Anne Boleyn.
There is debate but it's generally believed Henry VIII wrote it for Anne B.
As for this new Roslyn music, I wouldn't know. But I did enjoy listening to it.