NavList:

DavidC you wrote: I note that the check was made in 1977. What year diid the Admiralty stop testing sextants?     And why the Admiralty Compass Observatory?

They were calibrating sextants at least until 1981 as per the alternative photo I found. You might try looking at: https://en.wikipedia.org/wiki/Admiralty_Compass_Observatory  The parent department might have changed over the years, but everyone still called them the ACO, and they obviosly didn't change the certifictes each time the parent department changed.  You'll find more here:https://www.cambridge.org/core/journals/journal-of-navigation/article/div-classtitlethe-admiralty-compass-observatorydiv/A2858BB54D3A0E387B0EA4C04779E80E the abstract of which states: "The paper by Captain Cotter on Edward Johnson and the early history of ship's magnetism published in the September Journal sets the scene for the birth, in 1842, of the Compass Department of the Admiralty. Commander Fanning, a former Deputy Director of the Admiralty Compass Observatory, as it later became, here relates its subsequent history. The paper was presented to an Ordinary Meeting of the Institute held in London on 19 December 1979 with Dr J. F. Kemp in the Chair.

This paper traces the fortunes and development of a small department, one of the oldest Admiralty technical departments, from its early struggles with the magnetic compass, through many vicissitudes, economies, defence cuts, wars, intrigues, take-overs and even human frailties. We shall see how technical advances have led to ever more demanding requirements and I hope to show how, by meeting each new challenge, there has emerged the lively, forward-looking organization that today is still responsible for ‘everything that matters’ in navigation equipment, as it was at its inception in 1842."  (my embolding) 

You also wrote: Maybe I am reading the graph incorrectly but a 6' error at 60° seems massive for a precision instrument. Had the sextant been dropped?

No.  The foxing and the lack of a 0 before the decimal point make it hard to see, but  I read it as 0.6'. DaveP