There are still a variety of carols sung locally with local versions and tunes.

HOWEVER, versions of the words only of many hymns and carols were published from the 16th century on. This left singers without a given tune for them, and so favourite tunes were used (often folk melodies). For example, there were reputedly over 1,000 tunes in use for "While Shepherds Watched" (including one later used for a famous Yorkshire anthem). It wasn't until the publication of "Hymns Ancient and Modern" in 1861 that music was provided, and this served to standardise the music used for many hymns in many churches.

A&M didn't have many Christmas Carols, only about half a dozen of the ones we know, but ones commonly used for Epiphany, Easter etc. are now sung for Christmas ("The Holly and The Ivy" was an Easter carol) and subsequent hymnals (e.g. "The English Hymnal" and "Songs of Praise") included more carols, again with music.

Many of the carols we now use (over half, in fact) were written since 1861 anyway and these mostly had their own tunes. In the 20th Century, musicians like Elizabeth Poston and John Rutter also revived a number of medieval and antiquarian carols. Few of these had any music and so the melodies composed by Rutter or Poston have become the "standard" versions used for these.

All in all, nothing like so simple as "when did these become standardised", you see.

All part of life's rich tapestry, really.

:-)

PS. in Ashwell, we sing "We Three Kings" to the tune of "House of The Rising Sun" and "Away in A Manger" to "Green Grow The Laurels".