It’s twice over budget and four years late, but this futuristic £80m museum is a magnetic new presence on the Dundee skyline. No wonder Dennis the Menace has already moved in

Part cliff face, part galleon, the new V&A Dundee stands on the banks of the Tay like a curious craft sailed in from another realm. It is at once primal and futuristic, its great hull-like forms covered in slabs of gnarled concrete that fragment in places as they rise, as if already ruined. From some angles, the twisting mass reveals the gaping mouth of a cave. From others, it is like encountering the ribbed carcass of a beached whale, or the bones of a shipwreck.

It is a fitting form, given the rocky ride this £80m project has endured over the last decade, buffeted by multiple storms of cost escalation, construction delays and accusations of gross mismanagement. Originally planned with a budget of £27m, then £45m, and intended to rise out of the churning waters of the Tay, the building has retreated to dry land, and finally been completed at almost double the cost, four years late.

Facebook Twitter Pinterest Magnetic presence … V&A Dundee. Photograph: Murdo Macleod/The Guardian

“If we want to make something closer to nature than a building, then the costs are always unpredictable,” says Kengo Kuma, the feted Japanese architect responsible for summoning this great geological object from the riverbed. “We encountered many unexpected things along the way.”

The history of the project follows a familiar story of an inexperienced client seduced by a thrilling competition image and only worrying about practicalities later. An independent report published in 2015 listed a damning catalogue of failures in procurement, governance, project management and cost control. It concluded that the client body, Design Dundee Ltd (a partnership of the V&A, Dundee city council, Scottish Enterprise, the University of Dundee and Abertay University) had little chance of realising the building on budget from the start.

Play Video 0:35 V&A Dundee: drone footage of the museum seen from the air – video

But it stands there now, beside a similarly ambitious neighbour in the RRS Discovery, the ship that sailed Scott and Shackleton to Antarctica in the early 1900s. They are a pair of structures alike in their bravery-verging-on-recklessness.

Standing as two inverted pyramidal forms that join together as they rise, creating an archway that frames views of the river, Kuma’s building has a magnetic presence, enticing you to explore its chiselled clefts. It may no longer stand entirely in the Tay, but shallow pools of water lap at its base, while one prow plunges straight into the fast-flowing river, ensuring that much of the original intention survives. Bracing east-coast winds whistle through the tunnelled archway, reinforcing the elemental feeling of standing at the edge of the land – and encouraging you to seek swift shelter inside.

Facebook Twitter Pinterest Reckless bravery … the V&A Dundee alongside the RSS Discovery. Photograph: Iain Masterton/Getty Images

As you enter through a slanting triangular opening sliced beneath a deep overhang, the rough concrete panels give way to a warm, bright interior lined with layers of wooden flaps, set at odd angles as if caught in a breeze. Fixed with the same jumbled irregularity as the concrete cladding, this rippling panelled lining adds a surreal quality, as if you have just walked into a scaled-up model.

“I like to make my buildings out of particles,” says Kuma, who is known for cladding his structures with many small pieces, whether making a screen of tiles suspended in a wire rigging for his Folk Art Museum in Hangzhou, China, or bolting milky glass panels on to the facade of his FRAC art gallery in Marseille. “It avoids the big boring wall, and gives intimacy to a space,” he adds. “And it can teach us about depth, size and shadow. A white abstract box cannot teach us anything.”

Facebook Twitter Pinterest ‘The gaping mouth of a cave’ … ground level at the V&A. Photograph: Hufton Crow

These might sound like the gnomic pronouncements of a Shinto sage, but Kuma’s best buildings create richly layered spaces that delight in the effects of light filtering through their various parts. The V&A Dundee is more bunker-like than his lighter timber concoctions in Japan, and some of the details a bit more clunky, but the effects are there. The building’s angled stony strata catch changing light throughout the day and are illuminated through the reflecting pools by night; up close, their rough-cast texture echoes Scottish harling, forming giant cliff faces of pebbledash.

The cave-like entrance leads to a gaping interior volume, where a shallow black marble stair climbs around a large open floor taken up by a cafe, shop and ticket desk, while a long wooden bench rings the edge of the room. It is large and open enough to feel like a true public space for the city, influenced by project architect Maurizio Mucciola. “Being Italian, my reference for public space is a nice cosy square, like you get in Venice,” he says, “where you can just sit with a spritz and watch the world go by.”

Facebook Twitter Pinterest ‘A true public space for the city’ … the cladded interior of the V&A Dundee. Photograph: Hufton+Crow/PA

Opportunities to exploit the sloping structure to full effect have been sadly missed: one shallow raked wall would have made for dramatic stepped seating, but is inaccessible, while the actual auditorium is tucked into a prosaic box room upstairs.

Proceeding up above this generous indoor piazza, you come to the main event: two large gallery spaces, one dedicated to Scottish design, the other a column-free hangar of a room for temporary exhibitions, opening with the Ocean Liners show, which began in London earlier this year but is here given more space to breathe. At 1,100 sq m, equivalent to the V&A’s new subterranean extension in London, it is the largest museum-standard exhibition space in Scotland, and it will receive touring shows as well as initiate its own.

Designed by museum experts ZMMA, the Scottish Design Galleries are a tour de force, showcasing a dazzling array of 300 objects designed or made in Scotland, from Hunter wellies to the Duchess of Roxburghe’s diamond-winged tiara, and original Dennis the Menace artwork from the Beano, produced by Dundee-based publishers DC Thomson. A sci-fi Paisley cloak from a recent Star Wars film is a suitably futuristic accessory for Kuma’s stone spaceship, while a star of the show is Charles Rennie Mackintosh’s Oak Room from the Ingram Street tearooms, restored and on display for the first time in 50 years.

The display provides an illuminating lesson on the vitality and originality of Scottish design throughout the ages, which makes what is happening outside the window even more hard to swallow. While competition images and PR shots show the V&A building in splendid isolation, the reality is anything but. The view of the museum from Dundee’s Georgian city centre is already partially blocked by the hulking frame of a new hotel and offset by a garish new railway station, both part of a £1bn waterfront masterplan to “connect the city with the river”. As in many waterside regeneration schemes the world over, from Salford to Cape Town, this means the hasty erection of commercial buildings around the new cultural anchor, built under the banner of “bringing life” to the place. Sadly, it seems that all of the architectural effort has been lavished on the museum, with little care for how the rest of the pieces hang together.

Thankfully, Kuma’s concrete culture ship is tough enough to withstand whatever the developers want to throw at it.