This film is part of the Mirroring Tarkovsky season, a full BFI Southbank retrospective for the director which you can find the details for here. Stalker has various screenings from October 20th to November 7th and you can find those dates here.
Chicago Reader review:
Andrei Tarkovsky's 1979 masterpiece, like his earlier Solaris, is a free and allegorical adaptation of an SF novel, Arkady and Boris Strugatsky's Roadside Picnic. After a meteorite hits the earth, the region where it's fallen is believed to grant the wishes of those who enter and, sealed off by the authorities, can be penetrated only illegally and with special guides. One of them (Aleksandr Kaidanovsky), the stalker of the title, leads a writer and a professor through the grimiest industrial wasteland you've ever seen. What they find is pretty harsh and has none of the usual satisfactions of SF quests, but Tarkovsky regards their journey as a contemporary spiritual quest. His mise en scene is mesmerizing, and the final scene is breathtaking. Not an easy film, but almost certainly a great one.
Here (and above) is the trailer.