This film is part of the Big Screen Classics season at BFI Southbank (details here). This movie also screens on 11th, 21st and 24th April. You can find all the information here.
Time Out review:
Twelve Brechtian tableaux chronicle the life and death of a whore, starting out as a documentary on prostitution, ending as a Monogram B movie. In retrospect, Godard expressed doubts about the cheap gangster pyrotechnics as being merely a nod to cinephilia. But like the highly stylised prostitution scenes, they are in fact a distantiating device forcing a more direct confrontation with the film's true subject: the enigmatic beauty and troubling presence of Karina, and the mystery of Godard's own passionate involvement with her. This film, as Godard has noted, was the first stage in the inevitable dissolution of their marriage, as described in Pierrot le Fou; and every scene in the film obliquely pinpoints that crisis as originating in the awareness that, as director to star actress, he found himself rapturously but humiliatingly playing client to her prostitute.
Here (and above) is the trailer.