Two in the morning is when the autumn clock change lands — the moment the UK drops out of British Summer Time back to GMT, and the reason October's last Sunday is twenty-five hours long. Most phones handle it silently; oven clocks and car dashboards famously do not.
Otherwise this is the deepest part of the night for almost everyone outside a handful of trades. Bakers are already in, night-shift nurses are halfway through, and motorway maintenance crews work under floodlights during closures that only exist between about ten in the evening and five in the morning.
For parents of a newborn it is simply another feed, and for anyone lying awake it is the hour that feels longest. Counting towards it is usually about an alarm rather than an event — an early airport transfer, a shift start, or a medication schedule that has to hold to the clock rather than to daylight.
Common questions
Why do the clocks go back at 2 am?
It is the point of least disruption — almost no scheduled services are running, so the repeated hour affects very few timetables.