A court, like a prison and a sewage works, is one of those buildings with which we hope never to become too intimately acquainted. Its architecture appears only in our worst nightmares, fed by Bleak House, Kafka, Crown Court (for those of us bunking off school in the 70s), This Life, Judge John Deed and a million Hollywood pot boilers starring Harrison Ford. Inside they should be marble chambers and echoey staircases across which rival parties glare, and rival barristers flirt. There should be miles of labyrinthine, shadowy corridors, peopled by meek Miss Flytes and Ks, trapped, waiting for eternity for their case to be settled. Outside, the court should be stern, august: pillars, possibly pediments and, in Hollywood films, always with steps, on which the wrongly accused and rightly acquitted (both, generally, Harrison Ford) can face off the cameras. Above all they must be intimidating. And they should never, ever be painted primrose yellow.

Manchester’s new Civil Justice Centre — the largest court building constructed in Britain for 125 years — blows these clichés away. These aren’t courts. It must be an arts centre, surely, or the HQ for a glamorous brand. There’s that cheerful yellow, for a start, and no steps — this one’s informal, straight onto the street. There’s a café for Jarndyce and Jarndyce to vainly await judgment over a latte. And in place of columns, pediments and square-jawed stone, there’s — I believe it’s called avant-garde architecture, m’lud — looking for all intents and purposes like a deranged filing cabinet in a very messy brief’s office. This is justice, Aussie style.

Manchester’s CJC is the European calling card for Australian architects Denton Corker Marshall, a big, brash sunny firm equipped with all the Aussie stereotypes. Laid back? You bet. Barrie Marshall wears architects’ regulation black but splashed with primaries. Their architecture follows suit, hi-tech with day-glo highlights, like Norman Foster in a Hawaiian shirt and flipflops. Their talent is taking architectural shapes and zuzzing them up in the blender — a chunk of Mies van der Rohe, a splash of Will Alsop, a swoosh of Zaha Hadid, a lump of Dutch left-fielders like MVRDV and Rem Koolhaas, whipped into an architectural smoothie that may not be strikingly original, but is always striking. The CJC, with its jaunty angles and thoroughly un-Manchester colour, already adds an optimistically southern hemisphere note to a dun-coloured skyline more used to misery, rain and Morrissey.

To an ambitious architect, a court, especially one made up of 47 necessarily introspective courtrooms, 94 consulting rooms and a lot of corridors, offers a bleak prospect. 125 years ago, when Queen Victoria opened the Royal Courts of Justice on London’s Strand, its architect GE Street rationalised and centralised London’s Dickensian chambers in fashionable, lofty neo-gothic, sprawled around quadrangles and cloisters. The CJC also unites disparate courts, and acts as overspill for big London trials, but Barrie Marshall didn’t have Street’s luxury, with a tight site squashed beside the river Irwell. So he went up. And, in doing so, he says, “it all became clear. It gives you the space, and thinking space, to cut through the crap.” Denton Corker Marshall’s great strength is finding a simple, graphic form for what appears to be a worryingly complex function. Sometimes their grand gestures err on the side of the kitsch. Sometimes their over-eager form contorts the function. But not here. Liberated in the air, Marshall has pulled apart the red tape of a court and reassembled it in a novel form — concise, clear and cheerful, as far from legalese as it is possible to be.

Like an airport, the complexities of a court boil down to two things, public and business. In between, where they meet, is the courtroom. Marshall has simply split the realms into slices, assembled in what he describes as a “club sandwich, turned on its side and pinned together by toothpicks”. The slice of the sarnie to the east contains the judges’ quarters, retiring rooms, lounges for barristers, and those corridors. To the west is a stupendous 20-storey public atrium, with Europe’s largest hung glass wall, a sheer 60 square metres, on one side. In between there’s the meat, the central slice of the concrete core, rising 260 feet and containing the lifts, stairs, loos and circulation balconies looking out over the atrium; and then the main filling, the court rooms, a series of oblongs clad in two skins for acoustics and privacy, metal, painted in Mondrian-esque blocks, then glass, which burst out of the side in massive chunks, dangling, “look-no-legs”, 15m over the street below. More chip butty than club sandwich.

“Simple, simple, simple,” is Marshall’s mantra, from these basic forms, right down to the materials and colour schemes — white, white oak, aluminium grey and that primrose yellow - never overegged, designed instead to soothe the nerves. The simplicity means that Miss Flytes and Ks are never lost. So slim a building causes daylight to pour in from either side, right into the courtrooms, and with views far off to the Pennines, helps orientation. Gusts of natural ventilation run through the building like bronchial tubes via “wind grabbers” on the western façade, so it’s never fusty and the air con is, hopefully, rarely turned on. And it delivers possibly the best new public space in the city, the magnificent atrium, its loftiness relieved by randomly placed rectangular grey and yellow “pods”, containing consulting rooms and viewpoints, perched precariously on the “toothpick” beams.

Manchester’s architecture has been improving, slowly, steadily, from a very low base since the reconstruction after the 1996 IRA bomb. Most of it has been hype, guff about “urban renaissance” clouding some distinctly mediocre architecture, much of it jostling the CJC. This building raises the game significantly. It may look fun, but it’s dead serious, well-built and fit, hiding its complexity under a jovial façade, a bit like the Australian cricket team. Like all public buildings these days it’s privately financed, too, though its good detailing and well rounded architecture lift it far above most PFI dross to become one of just half a dozen decent public buildings commissioned by the government during the Blair years — and a surprisingly cheerful gift to mark the birth of that already-mocked, Orwellian new department, the Ministry of Justice. As in sport, it’s a rum day when it takes an Australian to come over here and tell us how to do public buildings with gravity and levity, but sure enough that’s what they’re doing, teaching old grandma to suck eggs. Denton Corker Marshall have won a brace of commissions in Manchester, and recently won planning permission for their somewhat less day-glo visitor centre at Stonehenge. LAB, architects of Melbourne’s defiantly whacky Federation Square, are designing Bristol’s massive new landmark city museum. Brace yourself. The Aussies are coming. And they aren’t coming quietly.

The CJC opens to the public towards the end of October.

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