For a long time, I believed the hey for three to be an original and typical English dance movement. But it appears already in the French dance book Orchésographie, which Jean Tabourot has published in 1588, under the pseudonym of Thoinot Arbeau. There he discusses with a student named Capriol the dances of his youth, among others a Branle de la Haye. Here is the translation of how he described the Haye:

Capriol : I cannot quite understand what you said about this haye.
Arbeau : You will understand it quite easily this way: imagine three dancers (the smallest number that can be), mark them with the letters A B C, and put them thus:

"Haye" is old French for a hedge, or a fence of woven willows (like a basket).

Now here is my description (which starts with the right shoulder):
Two person meet each other, a third person stands behind the middle one. All three move on the path of a large figure eight. On one side, they move around each other by the right shoulder, on the other side by the left shoulder. Whoever comes from the outside into the group, passes between the other two people.
If everyone would hold a ribbon hanging down from the ceiling, and the movement would be continued, these ribbons would be plaited into a braid.

An English poet once said, that angels in Heaven dance the hey on and on, singing the praise of the Lord. Here on Earth the hey is usually finished, when all returned to their starting places. In most cases. 16 beats are allowed for this.

Quoted from my book Leitfaden / A Guide to / Contra Dance (Volume 3)