Playford was history by Austen's time - like setting a film in the 1980s Manchester club scene and having a big band in suits playing Begin the Beguine for the dancers. There are lots of dance/tune publications of the period - Aird seems to have been the go-to source, and the number of booklets William Campbell managed to sell suggests that Scottish dances were hugely popular in 1800-ish England.

Minuets persisted at the top end of the market (I don't think the Playfords published many of those), soon to be eclipsed by the waltz after 1815.