Ah, the carol-singing tradition - that's another whole can o' worms! Love it - have only experienced it as "Carols in August" at Whitby and Sidmouth festivals, run by Ian Russell, but can imagine what it would be like in the pubs of Derbyshire and Yorkshire (and anywhere else) near Christmas.
And hymn melodies too: I can think of several tunes for a couple of hymns at least - All Things Bright and Beautiful, Love Divine, all loves excelling, and they each have their devotees.
And having just come through this year's Burns season, there are a good number of Burns songs that do NOT use the original tune, some of the latter being too big a range for the average singer: and then conversely, the same tune being used for 3 or 4 different songs.
Singing and dancing: I have also played in a couple of ceilidh bands, and some of the tunes we use are in fact song tunes: nice to see some of the fitter dancers managing to song and dance at the same time!