As your handy SMuFL guide will tell you, reversed time signatures represent ‘diminution’ – a reduction in the duration of the notes. (“Faster”, you could say.)
Playford’s Dancing Master was first published in 1651, so 1707 will be a reprint. By that time, the notation would be a bit old-fashioned.
https://w3c.github.io/smufl/latest/tables/medieval-and-renaissance-prolations.html