The hands are not setting themselves.

The controlling radio signal for the National Physical Laboratory's clock is transmitted on the MSF 60kHz signal via the transmitter at Rugby, operated by British Telecom International. This should have a range of some 1,500 km or 937.5 miles. All of the British Isles are of course within this radius.
The National Physical Laboratory's role as keeper of the national time standards is to ensure that the UK time-scale agrees with Co-ordinated Universal Time (UTC) to the highest levels of accuracy and to make that time available across the UK. As an example, the MSF (MSF being the three-letter call sign to identify the source of the signal) radio broadcast provides the time signal for, electronic share trading, the clocks at most railway stations and for BT's speaking clock.

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