In the three-part miniseries “A Very English Scandal,” streaming on Amazon Prime, screenwriter Russell T. Davies and director Stephen Frears tell the story of British politician Jeremy Thorpe and Norman Josiffe (later Scott), the former lover he allegedly tried to have killed.

Beyond the inherent drama and comedy, what interests Davies (the creator of “Queer as Folk,” who went on to remake “Doctor Who”) and Frears is the place the story holds in the legal and social history of homosexuality in Britain, a country where until 1967 same-sex sex could land you in prison.

Jeremy, played by Hugh Grant (who also starred in Frears’ 2016 film “Florence Foster Jenkins”), and Norman, played by Ben Whishaw, met in 1961. Norman was working as a groom at a country house where Jeremy was spending a weekend. The MP gave the stable boy his card, who looked him up in London, arriving with a suitcase and a small dog. (He has been, he confides, in a psychiatric institution; pills are duly taken.)

An affair began and ended. Norman, who possessed incriminating letters, began to seem like a threat to Jeremy, who had become the leader of the Liberal Party. He began to talk about having Norman killed: It would be “no worse than shooting a sick dog,” he infamously suggested.

With its kicky title fonts and jaunty score, “A Very English Scandal,” adapted from John Preston’s 2016 book of that name, takes a relatively light tack on the material, from which it occasionally descends into a darker place.

It bursts out of the gate, with an animated, half-coded conversation between Jeremy and fellow MP Peter Bessell (Alex Jennings) and continues to move fast. While nearly 20 years pass from when Jeremy met Norman to the trial that was their last point of contact, it feels more compact than that.

Grant does not attempt to look dapper or sway us with his patented half-shy smile. Indeed, at 57, he is perhaps a little worn-in for the part — Jeremy was in his early 30s when he met Norman and 50 when the case went to trial — but he is very good, marshaling his charm against other characters while letting the viewer feel the limits of that charm.

Whishaw, 37, keeps you guessing as to Norman’s motives and state of mind in a way that feels genuine; he earns your sympathy even when you’re not quite sure he deserves it. And the filmmakers are quite clearly on his side; even Jeremy’s friends and lawyer say nice things about him.

The character represents a first step into a freer future. “All the history books get written with men like me missing, so, yes, I will talk, I will be heard and I will be seen,” Norman tells the court, in as much as a speech as anyone makes here. If he is not always the best shepherd of his well-being, and liable to overstep himself, he is also the story’s more genuinely aggrieved party. He grows more solid with time, whereas Jeremy is ready to cut people loose when they no longer protect or serve or amuse him.

Davies and Frears fill up the corners of the story with a roster of British eccentrics — bumbling conspirators, a lord with a house full of badgers (David Bamber), Jeremy’s monocle-wearing mother (Patricia Hodge) and sometime jailbird lawyer (Adrian Scarborough) and a prejudicial judge (Paul Freeman, the villain in “Raiders of the Lost Ark”) — who make “A Very English Scandal” seem more lifelike than not.