The first reference to Alfred as "the Great" was in Book 26 of the Historiae Anglicae by Polydore Vergil published in 1534.
Note that it took a while for this epithet to take hold. Originally, he had no epithet, except "The Learned" from the Chronicle of Roger of Howden (1174-1201). Notably NONE of the major original histories of England describe him as "Great". This includes the following:
The Lambeth Chronicle (15th century)
Actes and Monuments by John Foxe
Chronicle of John Hardynge 1543
Annales of England John Stow 1592
Holinshed's Chronicles of England, Scotland and Ireland
None of these books describe Alfred as "Great".
The reason why he probably started to get singled out was because there was a lot of history about him, due to the Life written by Asser, and because there was a popular set of oral tranmission verses known as the "Proverbs of King Alfred". These proverbs were well known among the common folk and recited at entertainments, so he was kind of a folk figure.