Outdoor drama is a pleasure complicated by the plot twists of the season. A day of almost hourly showers left the evening air so ominously moist for Sherlock Holmes that the detective could reasonably have announced: “The rain’s afoot.” A deluge held off but gave way to such coldness that the smoke and dry ice in the production competed with the actors’ breath clouds.

Billed as “a new mystery”, the script by Joel Horwood is a sort of bridge between Conan Doyle’s A Study in Scarlet (1887) and The Sign of the Four (1890). The conceit is that we are seeing the “real” events that Dr Watson, frantically transcribing most of the play’s dialogue into a notebook, later published as the second Sherlock Holmes book.

But while he faithfully recorded some of the case – including jewels from an Indian Mughal treasure box sent annually to Miss Mary Morstan in London – we see that he falsified elements including the true persona of Holmes. Watson also left out – or Horwood has included – a subplot about stolen government military secrets that did not reach the Sherlock canon until the 1908 short story The Adventure of the Bruce-Partington Plans.

This suggestion of Watson as an unreliable narrator is one of many contemporary customisations of the franchise that also include Holmes’s belief that the British empire was itself a cunning fiction and reminders that the Indian gems are loot. An advantage of the alfresco setting is references to the nearby London zoo, Regent’s Canal and Baker Street, although the pace of the production by the appropriately named Sean Holmes was possibly due to the actors worrying about becoming frozen on the spot.

Joshua James’s perky, petulant Sherlock has some of the canonical props, including pipe and drug apparatus, but passionately embraces theories about the detective’s sexuality and neurodiversity with which earlier performers have only flirted. As Horwood foregrounds Holmes’s deductive outbursts – “That mud on your shoe is only found at the courthouse!” – there are torrents of ratiocination that James delivers with admirable clarity. Jyuddah Jaymes engagingly seizes the opportunities given by a Watson whose agency and braininess have been expanded from his Conan Doyle role of out-thought secretary.

Great characters out of copyright often suffer clumsy slander but, for all the eccentricities such as Sherlock Holmes and the Alien Abduction, the deductive genius has largely been lucky. Like Humphrey Ker and David Reed’s Sherlock Holmes and the 12 Days of Christmas last year at Birmingham Rep, Horwood’s version succeeds in simultaneously teasing and taking seriously the original.

• At Regent’s Park Open Air theatre, London, until 6 June