What was the archaic source of "All Turns To Yesterday"?
It turns out this poem is from the Vernon manuscript in the Bodleian Library, written in the late 14th century.
After a lot of searching on specific substrings I found that the lyrics sung by the Mediæval Bæbes seem to have been taken from Reginald Thorne Davies' Medieval English Lyrics: A Critical Anthology (1964). These particular verses are on page 118 of that book, but they're a fragment of a much larger poem.
The notes at the back of that book in turn somewhat cryptically cite it as:
Index 3996. Bodl. MS. (Vernon) Eng. poet 2.I (3938), f.408a. C.B. 14c., p. 143, no.101
which, so far as I can tell, means that it's #3996 in Brown and Robbins' Index of Middle English Verse and on folio 408.a of the Vernon manuscript.