The problem
Historically, the map at map.atownsend.org.uk didn’t change the URL as you moved around, and you had to press a “permalink” button to save the current location. This wasn’t ideal, so I had a look around for alternatives. Helpfully, the Leaflet site has a list of suitable plugins. Of those, leaflet-hash was suggested elsewhere. That seems to be still in use, although it hasn’t been updated for a while. It is spectaculary easy to use, and “does what it does” with no problems.
The challenge is that it stores the current location (for example “https://map.atownsend.org.uk/maps/map/map.html#11/54.4900/-3.1098”) but doesn’t store the current layer. That map currently has a choice of 5 base maps (test instances have 6) and 5 overlays: