I think this is most probably what MK is thinking about in the lines:
'A grinning mogul greets the crowd
At Execution Dock
All come to see three mutineers
Turned off at twelve o’clock'
An account from The Gentleman's Magazine, dated 4 February 1796, gives a vivid portrayal of a typical execution at London's Execution Dock.
This morning, a little after ten o'clock, Colley, Cole, and Blanche, the three sailors (Mutineers) convicted of the murder of Captain Little, were brought out of Newgate (Prison), and conveyed in solemn procession to Execution Dock, there to receive the punishment awarded by law. On the cart on which they rode was an elevated stage; on this were seated Colley, the principal instigator in the murder, in the middle, and his two wretched instruments, the Spaniard Blanche, and the Mulatto Cole, on each side of him; and behind, on another seat, two executioners.
Colley seemed in a state resembling that of a man stupidly intoxicated, and scarcely awake, and the two discovered little sensibility on this occasion, nor to the last moment of their existence, did they, as we hear, make any confession. They were turned off about a quarter before twelve in the midst of an immense crowd of spectators.
On the way to the place of execution, they were preceded by the Marshall of the Admiralty in his carriage (Smiling Mogul), the Deputy Marshall, bearing the silver oar, and the two City Marshals on horseback, Sheriff's officers, etc. The whole cavalcade was conducted with great solemnity.
The date 1879 is purely to give the listener the view he is thinking of the past and not a significant date with regards Execution dock. Hangings ceased at the dock in 1830....