Luminarium encyclopedia says : "Popular legend has it that "Greensleeves" was composed by King Henry VIII at the time of his wooing of Anne Boleyn. The song was entered into the Stationer's Register so late as 1580 [33 years after Henry's death] , as "a New Northern Dittye of the Lady Greensleeves", and was first printed in A Handful of Pleasant Delights in 1584. Its attribution to King Henry VIII is highly doubtful, though not disproved"
http://www.luminarium.org/renlit/greensleeves.htm

Alison Weir's "Henry VIII: the King and his Court" Page 131 says : " The King was also a 'fair' composer. 33 of his compositions comprising 13 instrumental pieces and 23 or 4 part popular songs such as 'Pastime with Good Company', 'Green groweth the holly', Alas What Shall I do for Love' and 'Whereto Should I express my Inward Heaviness?' were collated in the so-called Henry VIII Manuscript, where each is inscribed (not in Henry's hand, but probably one of his gentlemen), "The King. H.VIII". ....

She goes on to mention other songs which were erroneously thought to be composed by Henry and then says " Nor did Henry write "Greensleeves" which is probably Elizabethan in origin". Her source is a book by David Starkey called "Henry VIII: A European Court in England", which I don't own or I would look up what the primary source was that he used.

PS. I have been to Denmark and Sweden several times but not Norway. Scandinavian culture is quite fascinating. :)

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