This was originally inlcuded in one of the editions of John Playford’s book The Dancing Master or, Plaine and easie Rules for the Dancing of Country Dances, with the Tune to each Dance, 1651-1728.
If you go here: http://www.izaak.unh.edu/nhltmd/indexes/dancingmaster/Dance/Play4199.htm you can see its original notation with it’s original directions for the dance.
If you go here: https://imslp.org/wiki/The_Dancing_Master_(Playford%2C_John) you can view the text of one of the editions of the whole book.
Many of these dances were collected and re-popularized, along with the resurgence in the popularity of and recognition of the importance of “folk” music during the early part of the 20th century.
Cecil Sharpe( whose society’s website is linked here) was prominent in the recording and preservation of these tunes and dances English Folk Dance and Society
One of these publications, which was very important for our period, was the re-issuing of a manuscript collection of country dances found by Mrs W J Apted of Stevenage, Bedfordshire, in a cupboard of old books bought at a house sale for one shilling.
The manuscript contained eight collections of dances dating from 1774-1779.
The Apted Book of Country Dances (1933), reproduced 24 of these, and it was this book that the makers of P&P2 turned to when they wanted to recreate the dances at Meryton, Lucas Lodge, Mrs Phillips’s house and Netherfield:
Some fifteen dances had to be chosen, choreographed and rehearsed before filming could begin. Simon(Langton) recalls how they were put together: ” Jane Gibson had this wonderful book from the period called The Apted Book of Country Dancing which has all these Country Dances with instructions on how to do them. They have wonderful names like “The Shrewsbury Lasses”, “A Trip to Highgate” or “Mr Beveridge’s Maggot”
In actual fact Mr Beveridge’s Maggot is not in the Apted book!, but is in Playford.
Obviously the makers of Emma2 went to the same source, Playford.
As to the popularity of the tunes ,I’m afraid I cannot speculate how popular they were amongst Jane Austen’s contemporaries, and cannot think of a way to calculate this.
The employment of music and dancing masters during JAs era depended largely on two things;the depth of one’s pocket and the locality.