The Southern Region used a master clock system for most of the public clocks on the region. The master clock in the telephone exchange at Waterloo would produce a pulse every thirty seconds, which was distributed to all the sub exchanges around the region, which then distributed it via a number of clock circuits to all the clocks. These clocks were quite distinctive, as the minute hand stepped every half minute with a clunk. Rather than a traditional clockwork clock, where the minute hand moves gradually.
When clocks with second hands were introduced, these used mains power, but only to drive the seconds hand - the minute and hour hands were still driven by the pulses. If you looked at these clocks closely, the second hand would get to the 12 o'clock position, and pause briefly until the minute hand clunked round.
When the clocks were due to go back, the clock pulses from Waterloo were stopped for an hour. I understand that at one time this was done by simply putting a bit of paper between the appropriate relay contacts. When the clocks were due to go forward, the tech would just keep pressing the relay to generate extra pulses.
The master clocks were impressive pendulum clocks. I think Waterloo had main and backup master clocks. In addition, each local exchange had its own backup master clock, that could be switched in if the pulses from Waterloo were lost. Some bright spark had the idea of doing this automatically, with a circuit that monitored the incoming pulses, and automatically switched to the local master clock. Unfortunately, when the clocks were due to go back, and the tech at Waterloo stopped the pulses for an hour, this circuit then promptly switched over to the local master, and the clocks kept going!