Edinburgh has prefix N for there night routes
IIRC Edinburgh
used to have the 101-106 on Sunday to Thursday nights and the (improved) 202-206 on Friday and Saturday nights. Or could have been the other way round. But the routes were different to the "day" routes (with no attempt to mirror the numbers) and there was an enhanced service for the two busiest nights of the week. I think the Sunday-Thursday services were hourly from Waverley Bridge, but the overall network was nothing like as good as nowadays.
Sheffield had night buses in the nine hundreds, generally departures from the city centre at midnight and 02:20 IIRC (last departures in Sheffield were 23:15 for pretty much all routes, I think all Rotherham departures were at 22:45) - the days when pubs and nightclubs all closed at predictable hours made it a lot easier to find a critical mass of passengers for late services.
Then, in Sheffield, there were early morning services, numbered in the seven hundreds, a combination of more than one route in the same area, some big looping services ticking various boxes to ensure that people had some way of getting to their early shifts.
It's a tricky balance, the simplicity of replicating daytime services versus the need to spread resources over different suburban branches, whether passengers would rather have a regular late/early service on a handful of main corridors or have unfamiliar numbered routes (i.e. not replicating the "day" ones) that loop round to try to serve as many places as possible.
Didn't Reading stop their regular services around nine/ten at night and run "night" routes after that time? Or did they abandon that plan?