Entrapment is an ugly act, both for the trapper and the victim, though it remains a popular option taken up by newspapers and authorities alike to expose perceived crimes and misdemeanours. Tom Jacobson's two-hander, The Twentieth Century Way, dramatises the ‘cleaning up' of gay encounters by the police department in 1914 Los Angeles, basing his work largely on academic research by Sharon Ullman.

Their approach was to use actors to trick men into almost having sex – and then swiping their penis with an indelible marker pen to later prove their guilt as ‘social vagrants' in the most humiliating way possible. With more than 30 arrests and at least one suicide by a desperate victim, these police-led actors were clearly throwing themselves into their work.

Fraser Wall and James Sindall play the entrapment actors Brown and Warren, as well as a variety of cops, victims and other characters in this fast-paced production which – saving the tiresomely long opening pause – travels at a mile a minute.

Its premise is that Brown thinks he's auditioning for a film part, but is then challenged by rival Warren to improvise situations that might end up with a gay man being arrested. This layering of stories creates an absurdist drama where Brown, something of a faint-hearted victim himself, is ruthlessly manipulated into acting out increasingly explicit scenarios by the more experienced Warren.

There are some powerful scenes, including Wall's passionate pleas as the clergyman who can't bear to face life after his ‘crime' is made public, and Sindall's smooth-talking German dissimulator has a sinister charm.

It's not without comedy either – including James Sindall's demonstration of the capacities of the newly invented zip fastener, and how it facilitates speedy encounters as well as faster escapes from club raids.

The show is also handsomely designed by Joyce Rose Anne Robustelli, with snappy suits, stylish hair, and a wardrobe-rail of kimonos and silks which also serves as a convenient toilet wall in one of the entrapment scenes. Charles Parry's sound conjours the period with care, and Peter Harrison's lighting also contributes to the drama.

But perhaps there are just too many layers to this show, because ultimately it all feels a bit tricksy, and the relationship between the two men – once their true natures are revealed – doesn't quite ring true. Nevertheless it's crisply performed and tightly directed by Marylynne Anderson-Cooper, and has an important story to tell.

The Twentieth Century Way runs at the Jermyn Street Theatre until 28 January 2017.