The work -- which ran on Broadway for 1793 performances from 1978 to 1982 -- involves mystery-writing dramatist Sidney Bruhl (Russell Beale), who is drawing a mental blank for his next opus, but suspects he might be able to pull himself out of his dilemma when a student of his called Clifford Anderson (Groff) sends a promising commercial manuscript called Deathtrap.
The set-up, whereby Bruhl invites fresh-faced, evidently innocent Anderson to drop by with his only copy of that smash-potential play, immediately leads to a series of twists -- most unexpected, some signaled. In fact, all one can comfortably reveal about the convoluted plot is that Bruhl has a wife Myra (Skinner) with heart trouble, a cannily prescient Dutch psychic Helga ten Dorp (Parsons) living next door, a lawyer, Porter Milgrim (Beaver), who has his own powers of observations, and a household that is hung with a huge array of weapons.
Along with the chills and laughs Levin hands around like hors d'oeuvres with a biting after-taste, the frequent references to Bruhl's and Anderson's plays means there's a good deal of winking meta-theatrical talk about the challenges of writing workable mysteries. Levin's does hit the elusive mark, of course, especially given its gasper of a first-act closer.
On Rob Howell's shadowy deathtrap of a set, the troupe members go about their business with all the style an enterprise like this one requires. No matter what role just-this-side-of-corpulent Russell Beale is playing, he always slips into it as if into a tailor-made suit. Bruhl's tart comments slide off his tongue with ease, and the man's desperation comes from his center. Groff strikes Anderson's is-he-or-isn't-he-as-innocent-as-he-seems chord precisely right; Parsons displays her undiminished verve as the heavily-accented clairvoyant; Skinner's just-this-side-of-Lady-Macbeth wife is high-pitch-correct; and Beaver's lawyer is on the smart money.
Although Deathtrap is set in the year the play bowed and in a small town not far from New Haven, little about it has dated or seems overly American. (Yes, playwrights are more likely nowadays to think up their puzzlers on a computer than on the Smith Corona typewriter that Bruhl uses and praises, but so what?). It's sure to please Londoners, and will likely encounter another long run if and when it returns stateside.