Green’s Dictionary of Slang

Queen Dick n.

In phrases

in the days of Queen Dick (adv.) (also in the reign of Queen Dick) [Dick, i.e. Richard, being a man there could not be a Queen Dick]

at some unspecified, possibly mythical time.

1652		Laughing Mercury 25 Aug. - 8 Sept. 175: Erasmus of Rotterdam’s gib’d Catt, that kitten’d of an Irish hobby-horse in the yeer 1654, in the reign of Queen Dick.
c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Dick. That happened in the reign of queen Dick, i. e. never: said of any Absurd old Story.
1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn).
1811		Lex. Balatronicum.
1837		Dublin Eve. Packet 28 Jan. 3/5: An ill-favoured yahoo [...] thrust his raw physiognomy through the rusty bars of an old-fashioned gate, manufactured in the reign of Queen Dick.
1859		Matsell Vocabulum 71: queen dick Never. ‘It happened in the reign of Queen Dick,’ it never occurred; has never been.
1864		London Eve. Standard 13 Dec. 3/2: A bus driver in altercation with his conductor, who threatened him with ‘paying off’ soon, replied ‘Oh yes, in the reign of Queen Dick,’ which we found to be synonymous with ‘Never,’ or ‘Tib’s eve’.
1892		Aberdeen Press 20 June 2/4: Some of the vices hinted against the Catholic clerics may not, after all, have taken place in the reign of Queen Dick.
1895		Crowe Aus. Sl. Dict. 63: Queen Dick, it happened in the reign of Queen Dick, i.e., never.
1909		J. Ware Passing Eng. of the Victorian Era 208/1: Reign of Queen Dick (Peoples’). Never – a quibble.