I suppose a lot depends how you define 24/7. There are some which have a multi-hour break/ breaks overnight but some still call 24/7 like the Oxford Tube.
I imagine a lot of major airports have bus routes which operate 24/7 or close to.
Birmingham Airport has the X1 which operates hourly overnight.
Bristol Airport has the Bristol Flyer which operates hourly overnight.
East Midlands Airport has Skylink to Nottingham, and Leicester/ Derby which both operate at least hourly overnight.
Edinburgh has the Airlink which operates each 30 minutes.
Heathrow has the N9 to Central London each 30 minutes as well as some night coaches.
Manchester Airport has the 43 which runs at least every 30 minutes overnight.
Many of these will be under some special arrangement to run 24/7 as not many would be commercially viable operating to the airport between 10pm and 3am and from the airport between 12-2am and 7am.
Outside of airports, Bristol has quite a few.
The Bristol Flyer as well as the 43, 48, 49, 70 and 75/76.
Late night buses for Bristol & Bath Bristol & Bath have an extensive network of bus services which run after midnight, with several services running 24/7. So whether you’re using the bus to travel for work or for a night out, catch our late night services for a cheap and reliable journey home.
www.firstbus.co.uk
Cardiff used to have a couple, but none operate right now. The last buses end by midnight and don't start-up again until just before 5am.