Hapgood (Hampstead Theatre)

There's something unnerving about watching the recent past enacted. It's history, but not quite. In Hapgood, director Howard Davies emphasises this sense of dislocation through an aesthetic jolt: he lets Tom Stoppard's 1988 spy drama unspool in front of a giant state-of-the-art video wall, so it sounds like Smiley but looks like Spooks.

Naturalistic spies are usually painted as dour and depressing, but Stoppard describes Hapgood as an "entertainment" – and so it is, intermittently. The story is properly convoluted, with enough narrative surprises to feed the audience's hunger for thrills, and it maintains its grip despite being dialogue-heavy and prone to rapid-fire asides about particle physics.

Hapgood begins with a satirical re-enactment of that spy-story staple, the drop. A succession of shady characters enter the changing rooms of a swimming pool and exchange attaché cases. Spies spy and doubles cross. They all look the part: if not clad in black roll-necks and leather jackets they're dapper in Savile Row suits and tight black gloves (also leather). When the exercise is blown, the UK's control figure, 'Mother', has to go on a mole hunt.

Stoppard created this character well before Dames Stella Rimington or Judi Dench became secret service heads, even though no woman in either fact or fiction had previously held such a post. Mother, a.k.a. the eponymous Hapgood, is a heroine who – like almost everyone else in the play – may not be all she seems, and she gives Lisa Dillon a showy dream role that she grabs with élan.

There's even more prescience in the naming of Hapgood's colleague (friend or foe – for most of the play we aren't sure which), an imperious suit blissfully named Blair. An accident of nomenclature that may be, but Tim McMullan's reptilian performance makes it a snug fit. Blair is given to sardonic asides, as when he learns of the possible existence of twins in the KGB – "Now that's what I call a double agent".

Ridley and Kerner, played by Gerald Kyd and Alec Newman, are prime suspects (a phrase that sparks its own debate within the play) but then again pretty much everyone is painted in shades as grey as Ashley Martin-Davis's quick-change sets and Ian William Galloway's imposing video designs.

There's a DNA trail of Stoppardian wordplay all over Hapgood. (Do you dust a room or sweep it? Depends whether you're looking for fingerprints or bugs.) As a whole it spills too far into a parody to be genuinely tense, but it's often fun. And it's not only the Hampstead thinkerati who'll appreciate it: Hapgood's intrigues are a honey trap that should sweeten many a mood. Even the physics is tolerable, just about. When Kerner uses it to explain the failure of the drop it's a tack-on, but not a turn-off.

Hapgood runs at Hampstead until 16 January.