The Bun House is one of my favourite places in Peckham. It’s a local pub and art project space. The sense of community and the warm heartedness of everyone, especially Mick (the owner!) are truly genuine. Various events, performances and exhibitions populate the project room, the pub’s drinking zone and the outdoor rooftop terrace at the back.
SOAS university has a small gallery space dedicated to exhibitions about Asia, Africa and the Middle East. There's a small but beautiful Japanese zen garden on the rooftop (currently closed for refurbishment)
I vaguely thought about leaving London recently and the British Library came to mind as somewhere I’d miss. It’s an essential resource because it has almost everything. It also has some interesting exhibitions.