Alternate timeline (Republica)

Interference in Oliver Cromwell's death by the alien LeCompte resulted in an alternate timeline in which John Lambert became Cromwell's successor instead of Richard Cromwell. Lambert's superior leadership resulted in a version of the 20th century where Lambert's descendants ruled a Puritan British Republic as Lord Protectors. The Professor and Ace found themselves in this timeline and corrected it. (AUDIO: Republica, PROSE: Republica)

When speaking of various possible futures resulting from the English Civil War which he'd seen or heard of, the Second Doctor mentioned the possibility of "a triumphalist, hereditary Puritan Protectorate that rules the country until the twentieth century." (PROSE: The Roundheads)

Behind the scenes
The reference to this timeline in The Roundheads was to Mark Gatiss' unproduced novel Cromwell's Dust, originally intended to be a BBC Books release but later repurposed into the first The Time Travellers audio story, Republica.