Friday: It's free admission and a cheap bar at the Urban 75 Offline Brixton Ska Party Special at the Prince Albert, 9pm-2am.
Saturday: Watch International Horseball for free at Lee Valley Riding Centre (and Sunday 1.15-3.15pm).
The Rise of the Non-Conformists, Whitecross Street Party takes place all weekend creating an outdoor art gallery experience.
Get to a live site in Trafalgar Square, Woolwich or Walthamstow to celebrate 1 year to the Olympics or see what your local sport or leisure centre is laying on free.
Join Thames21 at the Tower of London foreshore as part of the National Archaeology Weekend, 12.30-2pm (and Sunday).
Ealing Blues Festival is in Walpole Park from 1-10pm, £4 adults, kids free.
Sunday: SHEDspace is a festival of art, food, music, fashion, film and sheds. Between 12-6pm, free admission to all sheds.
Islington Exhibits focuses on the south of the borough this weekend and you can join an exhibitions walk between 1-4pm.
Ealing Global Festival has the Wurzels headlining in Walpole Park from 1-10pm, £4 adults, kids free.
Monday: The Summer Skate Spectacular takes place at Lee Valley Ice Centre between 11am-4pm, skate sessions just £5 per person including skate hire.
Tuesday: LSE and BBC Radio 4 join forces for this evening's public debate: Keynes v Hayek - How do we get out of the financial mess we're in? Free to attend, starts 6.30pm, first come, first served at Old Theatre, Old Building LSE.
Wednesday: Take the Zero Hour Bus Tour from midnight till 2am - part of inTRANSIT festival. Free but you must book.
Thursday: It's family fun week with music, circus and animal games at the National Theatre's Watch This Space festival (weather permitting).
London on the Cheap is this week supported by Patron Social Club, who want to send you to the hottest music festival happening in London right now. Join for a chance to win tickets!