Of course Greenwich is really always "on time", since the Prime Meridian set here defines what time is for most practical purposes. The RO digital master clock registers it accurately, as your amusing piece admits, and the Shepherd electric gate clock repeats it to the public (in GMT all the year round) as it has since 1852.
There are many reasons why our other clocks vary; the "grandfather" in the Octagon Room because its mechanism has been removed: this, one of the original Observatory timekeepers of 1675 by Thomas Tompion, ticks on towards the Millennium on open display nearby.
Dr KRISTEN LIPPINCOTT
Royal Observatory Greenwich