The song came from John Northover, Uploaders, Dorset. May 1906. Two verses were collected by Henry Hammond, the remainder taken by Frank Purslow from a broadside. Several Morris sides dance to versions of the tune.
There are no nuts to be gathered in May. The children’s rhyme should be “Here we go gathering knots of may” which refers to the old custom of gathering knots of flowers on May Day. The ordinary phrase would be “to go a-maying”. (From a Times.co.uk online article)