What do you mean by "last extant"? It sounds too modern to have been an existing tune, unless Britten heavily modified a traditional tune. If so, what tune did he find to work from?

The text is also known by it's first line ("I come from heuin/heaven to tell"), and as such was published in William Sandys' Christmas Carols, Ancient and Modern (1833) and Edith Rickert's Ancient English Christmas Carols, 1400-1700 (1914), without tune. Sandys cites:

From "Ane Compendiovs Booke of Godly and Spiritvall Songs, collectit, &c. for avoyding of Sinne and Harlotrie," reprinted in "Scottish Poems of the Sixteenth Century," Edinburgh, 1801, vol. i, pp. 47-49.

"Followis ane Sang of the birth of Christ, with the tune of Baw lulalaw."

The site Hymns and Carols of Christmas says the text was "Based on Words: Vom Himmel hoch da komm ich her, Martin Luther, 1535". Since "Vom Himmel hoch" has been itself set numerous times, it would not surprise me if some of these were matched to the English text with the resulting pairing relabeled "Balulalow", despite having no derivational relationship to a Scots song or tune.

Here's a Scots version on YouTube: http://www.youtube.com/watch?v=K_eWSl9nBaM (sung by Camilla Mars)

I gather "balulalow" is a Scottish equivalent of "lullaby" or "hush-a-bye", so quite a few unrelated songs go by this same title, such as a famous setting by Peter Warlock (Philip Heseltine). Consequently, you'll probably have the best success by searching on variations of the first line. In my own searches at an earlier time, I came across a couple other settings of "I come from heaven" which were trad-sounding, but as they were also dull, I neglected to capture or even note the sources.