Gomme (1894-98) has:
partridge
turtle doves
French hens
colly birds
gold rings
geese
swans
maids
drummers
pipers
ladies
lords.

Gomme suggests that the song originated with the Twelve Days of Yule, an important mid-winter feast. Events occurring during those days were used to fortell the events of the future twelve months
(Keary, Outlines of Primitive Belief).
The song devolved into the Christmas game, and various forfeits were involved in the celebrations.

Gomme also gives the version of "Twelve Huntsmen with Horns."

Ring-necked pheasants were imported from China. I haven't checked for their first use in England.