Hugh Keyte and Andrew Parrot, in The New Oxford Book of Carols, say that the oldest preserved tune, from the Arundel MS, late 13th c. is possibly of French origin, but that the song was particularly popular in Britain. It's mentioned in Chaucer's Canterbury Tales, in the miller's tale. According to a tale in the 13th c. collection Speculum Laicorum, "Odo [of Cheriton] tells of a certain great cleric, Chancellor of Paris, who, among many other blessed things which he uttered, composed that sweetest song about the Virgin that begins: Angelus ad virginem."

This is suggestive that the original writer of the text and possibly of the preserved tune was Philip (Phillippe) the Chancellor. He often wrote texts for pre-existing tunes, particularly those of the monk Pérotin/Perotinus, but was also reputed to be a composer himself.

Keyte and Parrot reproduce (as song #144) the text from Sandys set to an arrangement of the tune Sandys printed for "When righteous Joseph wedded was", noting:

We take the melody and most of the bass (transposed down a tone) from Sandys's setting of 'When righteous Joseph wedded was'. He gives no music for 'The angel Gabriel' in his music section but prints it next to 'When righteous Joseph' in the body of his collection (a sign in broadsides, etc., that two texts share a melody): they have identical refrains and complementary themes, one the doubts of Mary, the other those of Joseph. There is no separate music for the refrain printed in Sandys's setting, though a double bar indicates the repeat point. (See also Gilbert's setting of 'When righteous Joseph', 129.)

Regarding this latter song, after some discussion of Gilbert's tune notation they write:

The tune appears in Bramley and Stainer's Christmas Carols New and Old (1871) as the 'Devonshire; tune for 'The angel Gabriel from God was sent' (144). Both carols were sung to either melody. (See also 'The Lord at first did Adam make', 141: II, which has a related melody.)

The authors constrast the style of Gilbert's setting of "The Lord at first" with Sandys's--the tunes themselves don't appear directly related. The Gilbert setting

with its speech-rhythm melody and splendidly free-ranging instrumental bass, represents a style of performance which one might not have imagined but for this example. Yet there can be no doubt as to its authenticity. There is no evidence that Gilbert, or those that assisted him, ever tampered with their musical sources; if they had, it is scarcely conceivable that they would have produced anything so outrageous, and performance confirms what the printed page suggests--that there is a rough, peasant musicality about the setting as a whole to which a middle-class Georgian editor could hardly aspire. Sandys's bass line is less surprising, though still undoubtedly instrumental.

Later, they add:

Sandys's tune is related to that which Gilbert gives for 'When righteous Joseph' (129); Sandys calls it 'a specimen of the old minor key, with a flat seventh at the close ... It appears harsh to modern ears, which expect G#' (D# in our transposition).