If this is anything more than an accidental parallel, we come back to an historical episode wherein the breaking down and rebuilding of London Bridge occur, and it looks as if the two streams down which this tradition has travelled, namely, first, through the game, and second, through the song, both refer to the same event.
Dr. Rimbault has, in his Nursery Rhymes, p. 34, reconstructed a copy of the original rhyme from the versions given by Halliwell and the Mirror, and gives the tune to which it was sung, which is reprinted [here]. The [tune from Kent] is the one generally used in London versions. The tune of a country dance called “London Bridge” is given in Playford’s Dancing Master, 1728 edition.[Addendum]
[4] Another informant gives the refrain, “Grand says the little Dee.”
[5] I have identified this with a version played at Westminster and another taught to my children by a Hanwell girl.—A. B. G.
Long-duck
A number of children take hold of each other’s hands and form a half-circle. The two children at one end of the line lift up their arms, so as to form an arch, and call “Bid, bid, bid,” the usual cry for calling ducks. Then the children at the other end pass in order through the arch. This process is repeated, and they go circling round the field.—Addy’s Sheffield Glossary.
See “[Duck Dance].”