This weekend the Luna Cinema is screening Groundhog Day (Fri 7 July), Arrival (Sat 8 July) and Top Gun (Sun 9 July) in Greenwich Park.
http://www.thelunacinema.com/greenwich-park/4592086264
The Rooftop Film Club is showing lots of films all summer on top of the Bussey Building in Peckham. The building is a three minute walk* from Peckham Rye, which is itself only 13 minutes from Blackheath station on the Victoria trains.
http://rooftopfilmclub.com/london/venues/bussey-building/
Pop Up Screens is showing Jurassic Park (Fri 25 Aug), Four Weddings and a Funeral (Sat 26 Aug) and Grease (Sun 27 Aug) in Manor House Gardens, which is listed as Hither Green but seems pretty Lee-ish. It’s a 17 minute walk from Blackheath station (according to Citymapper). You can also take the 202 bus to Stop F (on the opposite side of the road from the Sainsbury’s, Burnt Ash Road Lee Road (Stop ID: 58365), the 261 stops there too, then walk up a little bit to the crossroads and turn right into Taunton Road.
https://www.popupscreens.co.uk/tickets/events/upcoming/venue/4
All the open air cinema screening organisations listed, and many others, are showing other films across London and a reasonably complete list is here:
https://storify.com/jobrodie/open-air-cinema-screenings-london-2017
*Don’t forget that the last weekday train from Peckham Rye to Blackheath is 23:51 and you might need to allow a bit longer to walk back to the station as they close off the main cut-through back to the station. I discovered this last night after a lovely screening of Pride and Prejudice there (with a fun Q&A with Joe Wright the director beforehand) which has a run time of 2h 15 and began at 9.45. I’d allowed 10 mins to get back to the station and had quite the sense of humour failure when someone tried to redirect me to follow a different, longer route in an opposite direction, risking losing the train – fortunately I won that argument, they opened the barrier for me and I got the last train home.
Blackheath and beyond 