The most likely scenario on what little evidence is extant is that the song was like many other London stage songs 'Scotch', i.e., written in London with a 'Scotch' (i.e., Northern) setting. Martinmas was and always has been general British (if not European). It was the period when rural hiring fairs were held all over the country, presumably the Festival of St Martin.
Personally I think Ramsay's piece was that same piece sung by Mrs Knipp for Pepys, as most of the pieces published by Ramsay in Tea-table and Evergreen were straight from the London theatres. (Very little folk-material). So by say 1680 there were probably at least 2 versions floating about and which came first it is almost impossible to say now. The broadside is a little less flowery/stagelike but that doesn't really tell us any precedent.