Paging through the "Oxford Book of Carols" turned up quite a selection of carols sung in England in the 1700s and earlier. A few:

The praise of Christmas- In Pepys, some verses by Durfey.
God rest you merry, gentlemen
The seven joys
I saw three ships
Boar's head carol
Sir Christmas
Coventry carol (many, like the Wexford, Hereford,Sussex, etc., reached their printed form or were 'discovered' in the 18th c., it is doubtful that inhabitants of a named house would have sung any of them).
The first nowell
While shepherds watched
etc.

This readily obtained book is a good source; the notes help separate the reconstituted old, old but not known to the general public, from those that would have been well-known and sung in early Georgian times.