Hello G-OFUK,
The pilot should always set zulu time in the aircraft clock.
If you are using gps it is automatically updated with precise zulu time.
If the FMC is used it also uses gps to update, so it is also very precise.
If the pilot has to use the watch to keep time it should be updated eith precise zulu time by pilot within +/- 30 seconds (ICAO), which is also the accuracy with which the ATC reports time.
And it is always strongly recommended for pilots to always do a time check with ATC prior to flight to set Zulu time within +/- 30 secs. If it is done it will ensure proper and standard time keeping, no matter where you fly.
Hope That helped
Vicky