Actually, remove or alter the "N:" line in my ABC transcription. It seems that the poem appeared untitled in Kingsley's fairy tale "The Water-Babies" (1862[-3], printed serially in Macmillan's Magazine), where it was introduced as follows (bold emphasis mine):

[...] And soon my lady put a pretty little tombstone over Tom's shell in the little churchyard in Vendale, where the old dalesmen all sleep side by side between the limestone crags. And the dame decked it with garlands every Sunday, till she grew so old that she could not stir abroad; then the little children decked it for her. And always she sung an old old song, as she sat spinning what she called her wedding-dress. The children could not understand it, but they liked it none the less for that; for it was very sweet, and very sad; and that was enough for them. And these are the words of it: — [poem follows]

The poem was anthologized with the title "The 'Old, Old Song'" (with or without interior quotes), though I don't know if Kingsley himself assigned or endorsed this title.