Pastel pink and perfectly symmetrical, the Grand Budapest Hotel rises up from its painted alpine setting like something off a kitsch vintage biscuit tin. In the distance, among all the peaks, a funicular (actually a model) can be seen wobbling up a mountain. Meanwhile, staff wearing neat, brightly coloured uniforms scuttle about in carefully choreographed sequences: woe betide anyone who doesn't walk straight down the middle of a staircase. Yes, The Grand Budapest Hotel is a Wes Anderson film all right. From 1998's Rushmore to 2012's Moonrise Kingdom, the American indie director has made certain visual details his calling card, all of them meticulously arranged. One can only imagine how long he spends on his sock drawer.

It may seem obsessive – detractors might say irritating – but Anderson's visual obsessing has made him a cult figure, creating nostalgic, inviting worlds his fans relish diving into. The Grand Budapest Hotel is set chiefly in the 1930s in the fictional land of Zubrowka, a place Anderson calls "our own invented version of eastern Europe". It's also the name of a vodka, which is unlikely to be a coincidence (nothing is in an Anderson film).

Inspired by the writings of the Austrian Stefan Zweig, the film concerns the adventures of hotel concierge and bon vivant Monsieur Gustave (a wonderfully camp Ralph Fiennes) and his devoted lobby boy Zero (Tony Revolori). Gustave's beatific smile and genteel demeanour work harmoniously with the purple hotel uniforms (Anderson does love a man in uniform). He's also deliciously in sync with the hotel's pink exterior and the cakes from Mendl's, a near-magical patisserie that comes into its own after Gustave is accused of murdering one of his elderly lovers (Tilda Swinton in swathes of velvet). Mendl's candy colours contrast sharply with the gothic garb of our hero's enemies and the greys of the prison uniforms – as well as scenes showing the hotel later, in the 1960s, its opulence lost beneath a drab communist refurb.

"The idea was to make the hotel an embodiment of the world of Monsieur Gustave," explains Adam Stockhausen, the film's production designer and currently an Oscar nominee for his work on 12 Years a Slave. "Then, in the 1960s, to show how this world is lost. The change from the vibrant red lacquer of Gustave's concierge desk to the orange and green plastic of the 1960s lobby shows the change well."

Co-writer Hugo Guinness notes that the film's changing pace reflects the shifting focus of its story. "It starts off with a bisexual concierge inheriting a painting, then it becomes more of a caper, less rooted in reality. There's so much velocity: it starts off very literate and worthy, then gets faster and faster. That's what Wes was after: he wanted to speed things up at all costs."

And what Wes wants, Wes gets. "He is very detail-oriented," says Guinness. "Every little frame matters. He has a very clear image of what it's going to look like before he shoots it. He never stops, taking six to eight months to edit." Guinness and Anderson based Gustave on a mutual friend but, says the co-writer, "My job was to come up with the odd line or idea, and mostly be rejected. Wes was very much in charge. Once in a while, a little bit might get through the barrier, which was very satisfying for me." There isn't a trace of resentment in Guinness's voice: like Stockhausen, he clearly admires the director's love of detail. Any collaborator would have to.

"He plans and designs every single shot, which keeps you on your toes," says Stockhausen, who also worked on Moonrise Kingdom. "Complex sequences, like the introduction to the hotel in Grand Budapest, or the Bishop house in Moonrise Kingdom, involve multiple locations, stage sets, and often miniatures for certain shots. In addition to designing the parts, just keeping them right is a challenge."

Stockhausen talks me through a big Grand Budapest scene featuring a pink pastry truck parked outside the hotel, now taken over by an SS-like army. "This is the main entrance to the hotel after it's been occupied by the 'Zig-Zags' as a barracks. The Mendl's van is a vehicle we found and modified to look like a pastry delivery truck, not unlike a pastry box itself. I love the contrast between the tiny pink van and the grey-black army trucks."

The production designer clearly enjoys being part of Anderson's weird world. "The experience of actually making the films is remarkable. Each time, it's a journey: shooting but also living in the world of the film, far away from soundstages or other traditional moviemaking structures."

It seems logical that Secret Cinema have chosen The Grand Budapest Hotel for their next immersive cinema project, which will allow Anderson fans to follow cast and crew into his world; it should feel like a big-budget extension of all those Wes Anderson fancy-dress parties that hipsters have been throwing for years. Secret Cinema guests will likely be greeted with rich reds and pastel pinks, though Moonrise Kingdom would have been a different story: the green grass and the khaki of scout uniforms dominated the colour palette of this tale of runaways, while warm oranges and browns brought a cosy 1970s retro flavour to Fantastic Mr Fox. The Life Aquatic with Steve Zissou was awash with the turquoises of the sea and the red bobble hats of the eccentric crew. But it's about more than just colour: other visual motifs include long tracking shots, 90-degree whip pans and tilts, rostrum shots over miniature models, intertitles (font: Futura), montages, storybook stylings, and an almost Kubrickian obsession with symmetry and camera movement.

Almost. For, despite his fastidiousness, 44-year-old Anderson's direction is both humorous and self-aware, with deliberate quirks occasionally inserted to avert any feeling of idealism. Life for his gently browbeaten heroes is not perfect – and it shows. Take Owen Wilson's bandaged face in The Darjeeling Limited, or Saoirse Ronan's birthmark in The Grand Budapest Hotel: both are notably asymmetrical touches that jar with the film's framing.

Recurring imperfections in Anderson worlds include elusive fathers, dysfunctional families and awkward reunions (his father left home when he was young, poignantly leaving him with a Super 8mm camera). Like many auteurs, Anderson seems torn between rewriting his past and recreating it; between designed perfection and realism. The realities of The Grand Budapest Hotel are arguably the darkest yet: war, murder, prison. Accordingly, the film is more visually experimental. "There's even a black and white segment," points out Hugo Guinness. "I think Wes is taking more risks, he's trying new things. He's mid-career – more and more confident all the time."

It doesn't take a psychiatrist to suggest Anderson put something of himself into Gustave. A perfectionist, this old-school hotelier strives to make even the most uncivilised environment palatable: his delicate approach to serving prison slop brings one of the film's funniest moments. And a telling line said by one character about Gustave's desire to recreate a bygone era could almost be Anderson's own epitaph: "His world had vanished long before he entered it. But he sustained the illusion with a marvellous grace."

The Grand Budapest Hotel is in on general release on 7 March. Secret Cinema presents The Grand Budapest Hotel runs until 30 March