Not an open-air screen but Birkbeck Cinema is a small hidden gem within one of the buildings on Gordon Square (number 43). It is used by the students and faculty to show films relevant to the courses on film studies but there's also a small film club which shows films and then has a nice little discussion about them. I saw The Conversation there a year or two ago.
The Birkbeck Film Society on Facebook, and a page about their events / 2012 season. Bizarrely the film society has its own website but this doesn't appear to be active, Facebook's the best place to find out what's going on. The cinema also has a website of its very own too.
Birkbeck Cinema, 43 Gordon Square, WC1H 0PD
2012
Every Friday 20th January – 3rd March, screenings start at 6.30pm.
Gloria (John Cassavetes/1980/USA/123 minutes) - 20th January
Unrelated (Joanna Hogg/2008/UK/110 minutes) - 27th January
Touch of Evil (Orson Welles/1958/USA/112 minutes) - 3rd February
The Green Ray (Eric Rohmer/1986/France/98 minutes) - 10th February
Nuts in May (Mike Leigh/1976/UK/90 minutes) - 17th February
Reminiscences of a Journey to Lithuania (Jonas Mekas/1972/United Kingdom and West Germany/88 minutes) - 2nd March now 24th February
Beau Travail (Claire Denis/1999/France/90 minutes) - 24th February now 2nd March
Special Screening in association with The Coelacanth Journal: The Secret Life of Edward James (George Melly/1975/UK/54 minutes) - 9th March
16th March – TO BE DECIDED
23rd March – TO BE DECIDE
Films in red have swapped round, according to information here https://www.facebook.com/events/230086500413502/ (you may have to log in to read this).