No Sondheim fanatic will want to miss this. Burt Shevelove's extremely loose adaptation of the ancient Aristophanes comedy was first performed in 1974 in the swimming pool of Yale University - the original chorus included Meryl Streep and Sigourney Weaver - and featured only half a dozen musical numbers; this however is the 2004 Nathan Lane adaptation for New York's Lincoln Centre Theatre, for which Sondheim created a further seven songs to punch up the size of the score.

That doesn't make The Frogs a traditional musical though: just as real frogs are amphibious creatures, able to thrive on land or in water, so this esoteric, quirky piece defies generic classification, being neither a fully integrated musical nor a straightforward version of the classical comedy. The bare bones of the story remain essentially the same: Ancient Greek God of theatre and wine, Dionysus, bemoaning a world full of fear and confusion, travels with his servant Xanthias to Hades (or Hell) to rescue his favourite playwright (in the original, Euripides, and in this version, George Bernard Shaw) from the jaws of death, and encounters a chorus of derisive frogs en route.

There are plenty of modern references shoe-horned in - Trump is, perhaps inevitably, referenced at one point - and the exhortation to act against what one knows to be wrong does feel particularly timely. The anachronistic script is more mildly amusing than genuinely funny however, and the overlong second half is stopped in its tracks by an interminable battle of wits between Shaw and Shakespeare, although it does culminate in a lovely musical setting of the "Fear no more the heat o'the sun" speech from Cymbeline.

Lane himself played Dionysus on Broadway, and the role is taken here by the magnetic Michael Matus, who possesses a beautiful, supple voice and impressive comic chops, whilst also bearing a strong resemblance to Lane. George Rae is a poignant and winning presence opposite him as undervalued slave ("I prefer 'P.A..'") Xanthias. They make a delightful double act. Emma Ralston is a lot of fun as a dominatrix version of Pluto, ruler of the Underworld, as is Jonathan Wadey - apparently channelling Michael Keaton in Beetlejuice - as other-worldly boatman Charon. The singing throughout is superb, and the quartet of musicians do sterling work - Tim Sutton is the MD and is also responsible for the exquisitely pared-down orchestrations.

The sophisticated score may not be vintage Sondheim but it is unmistakably the work of the master, with its jagged rhythms, complicated melodies, unexpected fugues and moments of breathtaking lyricism. Matus' gorgeous bittersweet lament for his lost love Ariadne is a particular highlight, and the lyrics are as tart and elegant as you'd expect.

Tim McArthur's witty, whip-smart choreography does a wonderful job of making the Jermyn Street stage seem larger than it really is, and Grace Wessels' direction has touches of real invention - such as the simple but effective creation of Charon's boat - although is played resolutely out front, which is a problem given that the auditorium has an entire bank of seats to the one side.

I was also a little baffled by the first appearance of the chorus: their jerky neck movements, guttural vocal ululating and copper coloured masks suggests a brood of hens rather than an army of frogs, but the capture of Dionysus by their enormous leader is cleverly done.

If ultimately The Frogs doesn't fully satisfy either as satirical comedy or musical romp, it is always fascinating to hear an unfamiliar Sondheim score, and the resonances within the story to the current political and socio-economical climate feels surprisingly unforced. A pleasant, intermittently rewarding evening.

The Frogs runs at the Jermyn Street Theatre until 8 April.