Lee Macdonald and I have had some email discussion about this. We’d both heard the story. I think I may have heard it in a lecture to the SHA, but can’t remember any more details.
We think it might have been the mirror for the Isaac Newton telescope rather than the JKT.
Lee also points out that “the Royal Greenwich Observatory was not run by the Admiralty in the 1980s. The Admiralty relinquished it in the mid-1960s and by the mid-1980s the RGO was part of the Science and Engineering Research Council.” But ties and loyalty to the Admiralty might still have held.