Bruce explained about the tune earlier in this thread, as GUEST points out.  A number of versions of  The blind beggar's daughter of Bethnal Green  have been found in tradition; the one in the DT was collected by Dr. George Gardiner from George Digweed of Micheldelver, Hampshire, in 1906, though the file makes no mention of this.  Click to play Midi.

Two tune variants found by Lucy Broadwood in Surrey were published in The Journal of the Folk Song Society (vol.1, no.4, 1902).

Malcolm