The Isle in this Southwark Playhouse production of The Tempest is certainly 'full of noises'. When the largely percussive music that punctuates the entire show is in full swing it feels as though we're hearing Caliban's 'thousand twangling instruments' humming, beating and sometimes crashing about our ears.

Composer Candida Caldicot's imaginatively scored sounds – performed by engaging musician Andrew Meredith and ably supported by the ensemble cast – quickly establish the eerie sense of magic and otherworldliness that's so essential for a successful Tempest.

Ariel, played as a muscular but anguished spirit by Peter Caulfield, has a thrilling singing voice which also brings its own ethereal beauty to the island, though some of the tunes for his songs seem a little haphazard. His strong physical performance contains some extraordinary contortions, aided by designer Ele Slade's plush costume which has him laced into a black velvet straightjacket. Her pared down set and costumes are perfect for the space, and make the ensemble's frequent character changes visually easy to follow.

Sarah Malin brings authority as well as humanity to Prospero – plus amazing cheekbones sharply emphasised by lighting designer Sarah Readman. She manages the mix of loving parent and vengeful magician with gravitas and humour, and her closing speeches in particular are beautifully judged.

The romance between ingénues Miranda (Gemma Lawrence) and Ferdinand (Benjamin Cawley) is tender and touching, and while some of the rich comic potential of their relationship is lost, they radiate the wonder and awe of love at first sight. Both take on two other roles, and make a successful drunken partnership as Stephano and Trinculo.

Anger and resentment ooze from Stanton Plummer-Cambridge's Caliban, and though the only real nod to conveying this creature's monstrous physical form is a hefty pair of rubber gloves, he creates a sense of real and present danger to Prospero. Plummer-Cambridge also plays Alonso, and the reunion between the grief-stricken father and the son he thought was drowned is one of the production's strongest moments.

Director Amy Draper has used every inch of available space to great effect, with the breath of Prospero's magic scattering the cast to all points of the compass. Her production is intensely physical too, with movement director Chi-San Howard contributing a wildly abandoned dance for the island's revels.

And although it takes the ensemble a little while to build their magic, this 90-minute show delivers an enchanting and emotionally charged Tempest.

The Tempest runs at Southwark Playhouse until 28 January.