As a piece of seemingly vacuous art work, Rupert Goold's production of this stunning high-concept musical with an uncompromising, insidious electronic score, is one of the most original in recent years: creepy, beautiful, reverberative, hollow, sleek and disturbing. It's Sweeney Todd for the MTV generation, murder with designer labels, hatchets with handbags.

Based on Brett Easton Ellis' virtuoso 1991 novel about a wealthy psychotic Wall Street trader, Patrick Bateman, who rips through the empty shell of his life with prowling, pornography and perversion, the musical goes even further than Mary Harron's movie version (starring Christian Bale) in providing a blank portrait of narcissistic numbness; and Matt Smith, giving a quite different performance of oddness and alienation to his Doctor Who incarnation, achieves what you might think of as the impossible: a fascinating shadow.

Partly this is because Smith, physically both utterly controlled and zombie-like, is a chief exhibit in a museum of his own imagining, and partly because the integration of Es Devlin's uncontaminated laboratory-style design, Katrina Lindsay's brilliant costumes and the deadening but ever witty pulse of Duncan Sheik's music and lyrics create an ironic aesthetic of chill, deliberate horror.

There are cultural references in the music – to the iconic kitsch 1980s sounds of Tears for Fears, Phil Collins, Whitney Houston and, most emphatically, Huey Lewis and the News – and the musical (unlike the film) preserves the spooky encounter with Tom Cruise.

But nothing obtrudes in the staging, and the book by Roberto Aguirre-Sacasa evokes such memorable elements as designer visiting card envy, "hard body" dreaming in the gym and on the dance floor, cocktail-sipping club land and coke-sniffing dives, all-in-a-line yuppie chit-chat, the density of the Gatsby-like social whirl and empty hedonism.

Content is so perfectly tailored to the design that Lynne Page's choreography – at one point Patrick and the traders are suspended horizontally by their work stations – is as much an organic statement of the show as the book and lyrics, just as the cast, individually and together, seem united in tone and purpose.

The violence is the choreography, too, as are the sexual encounters (one of them a threesome involving a giant pink panda), the chainsaw chase around and the constant undercurrent of ambiguity, amorality, identity confusion; it's hilarious that Patrick even magnetises the identities of those he obliterates.

Smith heads up a high calibre ensemble moving like a machine between the Harvard and Yale Clubs, Barney's (there's a great number with those bags on their heads), the Canal Bar, Dorsia and the uptown apartment where Patrick gets down and very dirty.

Susannah Fielding is Patrick's supposed fiancée, Katie Brayben a girlfriend, Cassandra Compton his over-devoted secretary and Ben Aldridge, Charlie Anson, Eugene McCoy and Hugh Skinner four of the oafish high-flyers who satellite their emblematic peer group leader. All the blood is tastefully done, spots of it seeping through a white sofa just as the globules drip from the movie credits.

Listen to our podcast: Edward Seckerson meets Duncan Sheik and Rupert Goold