That happened in the reign of Queen Dick—i.e. never; there never was a Queen Richard.
(Richard Cromwell, 1626-1712.) (1) Dick's hatband, which was made of sand. His regal honours were “a rope of sand.” (2) As fine as Dick's hatband. The crown of England would be a very fine thing for anyone to get. (3) As queer as Dick's hatband. Few things have been more ridiculous than the exaltation and abdication of the Protector's son.
(4) As tight as Dick's hatband. The hatband of Richard Cromwell was the crown, which was too tight for him to wear with safety.
= Richard. The diminutive “Dicky” is also common.
Jockey of Norfolk [Lord Howard], be not too bold, For Dicky [or Dickon], thy master, is bought and sold.
Shakespeare: Richard III., v. 3. (Dickey or Dickon is Richard III.)
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894