Britain has a strange relationship with its most distinctive film auteur, Peter Greenaway: fêted, celebrated, but also hated. For some, he is the epitome of arthouse aesthetics. His style is instantly recognisable: visually explosive films that resemble moving baroque paintings, characters embroiled in labyrinthine plots. The alphabet, lists, numbers and librarial taxonomic sequences provide narrative structures that unspool into sexual intrigue and death. British character actors deliver chilly performances, and nude extras abound.

He is recipient of a BAFTA for Outstanding British Contribution to Cinema, and the BFI is currently running an extensive season of screenings of his work, in celebration of his 80th birthday. Yet, despite these honours, his work has had patchy distribution in his country of origin. Since the turn of the millennium, and the tepid commercial success of the 1996 erotic tragedy The Pillow Book, his films have largely evaded British public consciousness. Critical reception has ranged from astonishment to derision at Greenaway’s perceived emotional shallowness, problematic misanthropy and—most criminally for the British—for being too clever by half.

Reciprocally, Greenaway has had an uneasy relationship with Britain. He has long projected an image of “Europeanness” in his themes and references, and he has lived and produced his work in the Netherlands for some time (not least because funding for avant garde film is more realistically available in mainland Europe). But, on a certain level, Greenaway’s films are as British as Monty Python. His middle period films (before the 1980s hits) have a superbly dry sense of humour, such as 1978’s Vertical Features Remake the mockumentary about editing images of perpendicular things in the English landscape, or the sprawling The Falls from 1980, a biography of 92 people affected by a minor apocalypse, the “violent unknown event”. This work seems to foreshadow the very British notion of Hauntology, with its public-information-film tone and creepy-hilarious, future-past setting.

Greenway’s more conventionally narrative films take a peculiarly British approach to setting, storytelling and tone. They resemble satires of genre: crossword puzzles displayed in ornate frames. Take, for example, his first “real” feature, The Draughtsman’s Contract from 1982, which has just been released in a remastered version by the BFI. The year is 1694, and Mrs. Herbert, the aristocratic wife of a cruel and frequently absent husband, commissions fashionable society artist Mr. Neville to sketch the estate of their country house (the fictional but plausible Compton Anstey). These drawings are ostensibly a reconciliatory gift. The terms of the contract for supplying them are not just provision of payment and board, but also that Mrs. Herbert must “meet Mr. Neville in private and comply with his requests concerning his pleasure”. The drawings and coercive sexual encounters go ahead as planned, until the body of the missing Mr. Herbert is dragged from the estate’s moat, at which point suspicion of murder falls on everyone, and tables are turned on the draughtsman. The film’s manipulative, vain male characters get their comeuppance at the hands of women far cleverer than them (a recurring Greenaway trope).

Superficially, this synopsis might sound like a straightforward, if edgy, British period drama. But in practice, it is an outlandish game. The dialogue is mannered, and the plot is strewn with a complex web of clues, like objects in an allegorical painting. Symbolic references to fruit punctuate the script (the film begins with a story about plums and ends with a chunk of pineapple being spat out). An inexplicable “living statue” inhabits the gardens. Michael Nyman’s score is a hyper-baroque illusion, mutating genuine 17th century themes by Henry Purcell through the use of anachronistic saxophones and pumping electric basso continuo. (Nyman was Greenaway’s composer of choice for his 1970s/1980s films, providing music that perfectly mirrors the films’ saturated bombast, before the two severed ties in the early 1990s.)

Most of all, the visual style emphasises the unreality. Characters are colour-coded in black and white costumes, set against the vivid green of the English countryside. The wigs are cartoonish in exaggeration. Many shots are perfectly symmetrical or seen through the grid of the draughtsman’s viewfinder.

Viewers viewing viewers: Greenaway’s implication of the audience as voyeurs of his spectacular images is another recurring theme in his work. At the end of his most commercially successful picture, 1989’s The Cook, the Thief, His Wife & Her Lover, a velvet curtain swings shut in front of the camera, a final reminder of the artificiality of what’s passed before: Michael Gambon as a vicious gangster and owner of a swish restaurant, whose cronies dress as if they’d stepped out of Rembrandt’s The Night Watch (costumes by Jean-Paul Gaultier), a choirboy as kitchen porter, and Helen Mirren escaping into the dreamlike space of the startling white, cavernous restaurant toilets to conduct an affair. In other films, like 2012’s Goltzius and the Pelican Company, a secondary audience even appears on screen.

This illusory nature of Greenaway’s work comes from his insistence on the visual primacy of filmmaking. He has repeatedly stressed his credentials as an artist, utilising film in the manner of a painter (the drawings in The Draughtsman’s Contract are his own) and delivering talks with provocative titles like “Cinema is Dead”. But this is just him throwing us off the scent, the trickster: Greenaway is steeped in the language of the moving image.

All this complication and obfuscation is one of the reasons for Greenaway’s difficult reputation. A filmmaker such as David Lynch is arguably just as “difficult” in terms of unpredictable narratives and use of media, but Greenaway’s British sensibilities and academic demeanour give off a whiff of being highbrow for the sake of it, needlessly self-indulgent. Additionally, the graphic nature of some of his 1990s projects soured the critical view of him. His 1980s work had captured something of the flashy zeitgeist, but now he seemed a bit nasty. In particular, there was widespread revulsion following 1993’s The Baby of Mâcon, which framed hard-to-watch violence with Greenaway’s icy, stylised mise-en-scène. A 1991 television commission for Channel 4, M is for Man, Music, Mozart (in collaboration with composer Louis Andriessen), also provoked tabloid horror, with its tableaux of dozens of naked actors.

Greenaway seems unbothered, and has continued to produce work on an ambitious scale, such as the early 2000s multimedia film trilogy The Tulse Luper Suitcases, and with technically ambitious ideas, such as his film installations projecting images onto pre-existing work by Leonardo and Rembrandt. Little of this later work has been screened in the UK, although the features and early short films are gradually being made available online through the BFI Player website. Some Greenaway “classics” were not even made easily available on DVD/Blu-ray, such as the kaleidoscopic Prospero’s Books, a 1991 retelling of Shakespeare’s The Tempest, featuring a wonderful performance by John Gielgud in a multi-layered, screens-within-screens cinematic world.

On these shores, he is an artist whose name is known better than his work. It’s our loss, of course. Whether you find his work enchants or repulses, Greenaway’s films should be a little more accessible to us – and appreciated as an uncompromising, stubborn, individual act of begrudgingly British creativity.