What sort of pattern dances are you familiar with/aware of, and are any of them 'called'? Do you have references that I can read further on?
Some good friends of ours have run a dancing group called London Barndance Company (https://www.barndance.org/) for 30+ years that meets monthly in London, not too far from Regent's Park. Visitors are welcome, if you go say Alan sent you. :-)
The dances tend more towards line dances than square dances, partly because line dances fit the hall better and also because of a belief that it helps keep the overall group together by mixing up the dancers. The bands and callers change from month to month, and with it the dances change as well. Mark's calls to the Wizard Walk (https://youtu.be/5hh4FgsGCrc?t=141 for the music ) may well differ from Colin's steps, and Mark's may even differ from session to session. Calls tend to go on for the first half of the music, and then people settle into the pattern. Here's a recent video shot by the band at a recent LBC session: https://www.youtube.com/watch?v=J8sEl_cF-J0.
There are dance socities that tend to a more regimented set of dances. From what I understand the "Playfair crowd" and many of the distinctly ethnic dance groups (Slovakian, Scottish) are in this camp. For more info, the society that owns the dance hall used by LBC and many othr dance groups may be helpful: https://www.efdss.org/.
And just for good measure, I should probably mention the dance
book written by my sister and brother in law, though I think there
more coverage of the historic steps than the manner in which they
were called:
https://www.amazon.com/Western-Dance-1450-1650-Complete-Anachronist/dp/B001H8XLLO
Alan