The Nine Muses, John Akomfrah, 92 mins (PG)

For a long time, British film has seemed to stagger from doom to reprieve to doom to reprieve. There was a period a few years ago, early in the history of the now-disbanded UK Film Council, when it looked doubtful that innovative or left-field film-makers could ever again count on getting a firm foothold in the British cinema scene. By and by, things changed, and over the past couple of years we've seen enough adventurous work to suggest that it was once again permissible for British films to be challenging and non-conformist. A few recent titles: Tinker Tailor Soldier Spy, We Need to Talk About Kevin, The Deep Blue Sea, NEDs, Tyrannosaur, Shame, Wuthering Heights, Kill List, Weekend, The Arbor ....

And then suddenly we seemed to be back on the brink of doom, with David Cameron's statement earlier this month – prior to the publication of the UK Film Policy Review – that public money, now distributed by the British Film Institute, should go to "commercially successful pictures". Much anguished commentary followed, because of the suggestion that he was effectively giving the thumbs-down to anything that wasn't The King's Speech – or, at least, that wasn't a box-office cert from the off (which no film, not even the most hard-nosedly commercial, can ever be).

And now reprieve again, apparently. The Review itself, published last week, actually brought some hope, not least in the recommendation that, as its chair, Chris Smith, put it, funding should go to "the widest possible range of movies ... from overtly commercial to overtly arty."

Before this statement was made, I was prepared to present this week's review as a ceremonial farewell to the sort of British picture that had seemed to be getting the official kiss of death. The Nine Muses is hard to categorise: part essay, part documentary, wholly film poem, if you like. Its director is John Akomfrah, formerly a mainstay of the group Black Audio Film Collective, whose montage film Handsworth Songs was a highlight of Eighties cinema's musings on multi-ethnic Britain and its history.

The Nine Muses is an archive assemblage tracing the history and imagery of black and Asian immigration to Britain in the Fifties and Sixties. It's also a reverie inspired by Homer's Odyssey and structured around the names of the nine Muses who, according to Greek myth, were the daughters of Mnemosyne, goddess of memory. Hence, some names that you'll know (Clio, muse of history, Terpsichore, muse of dance) and some that you probably won't (take a bow, Polyhymnia, muse of sacred song).

It's not always obvious how the Muses' presiding spirit (each section is named after one) relates to the archive footage: what, for example, Urania, muse of astronomy, has to do with shots of an ancient bathroom with mouldering lino, or of depressed-looking donkeys huddled in the wet. A selection of literary readings – Milton, Beckett, Emily Dickinson et al – offers oblique soundtrack commentary. And running throughout, in illustration of the Homeric theme of wandering, is a series of tableaux in which parka-clad figures stand in snowbound Alaskan settings. These enigmatic and breathtakingly desolate images, shot by Dewald Aukema, seem to embody an idea of Absolute North, or of the cold, compassless exile that Britain might resemble to immigrants from warmer places.

The film also offers historical images of a Britain desolate in more than weather: footage of the perennial Man in the Street grumbling about immigration; "Keep Britain White" daubed on a wall; an Asian family arriving in Birmingham, with aerial shots of the Bullring at its most glumly geometric. What makes all the film's archive images new is that Akomfrah juxtaposes them with literary voices largely (but not exclusively) associated with the classical and, more generally, white Western tradition (although Rabindranath Tagore, Chinese poet Li Po and others are quoted too).

On one level, it's clear what The Nine Muses is about: migration as real historical experience and broader mythical idea. But exactly how the film expands on its theme is something for the viewer to unpick. It's hard to get to grips with Akomfrah's elusive, allusive film, or to do more here than describe it or compare it to, say, the more abstruse docu-essay/travelogues of Chris Marker, or to the more straightforwardly personal Of Time and the City, Terence Davies's archive homage to Liverpool.

Haunting and hugely distinctive, The Nine Muses is just the sort of defiantly non-commercial film that comes under Chris Smith's "overtly arty" bracket; for the record, it was made under the aegis of the now-defunct UKFC and of the Arts Council. Such work no doubt falls way outside David Cameron's favoured image of Britfilm, and I was all ready to commend The Nine Muses as probably, regrettably, the last of its kind. Well, you never know, but last week's report holds out hope – so let's think of Akomfrah's remarkable film as, among other things, a poetic provocation for the future.

Next Week

Jonathan Romney watches George Clooney go Hawaiian in Alexander Payne's The Descendants

Film Choice

Michael Fassbender bares his soul – and more besides – in Shame, Steve McQueen's intense drama about sex addiction. Also starring, a wilder, edgier Carey Mulligan ... But the week's really sombre stuff comes in pen and ink, in Tatsumi, Eric Khoo's animated tribute to the grim tales of a Japanese anime master.