"While Shepherds Watched Their Flocks By Night" is #20 in the Shorter New Oxford Book of Carols (1993). There are several settings of the song in the carol book, and tune #5 is Cranbrook. So, I suppose it must also be in the unabridged New Oxford Book of Carols, which I couldn't afford.

You'll find only one version of the song (not Cranbrook) in the previous (1928/1964) edition of the Oxford Book of Carols. Nowell Sing We Clear (a quartet including Mudcatter Anglo), have recorded at least a couple of settings of the song, including Cranbrook.

-Joe-