The Bermondsey Street Festival looks like a fun, free pick for the kids this weekend. According to Time Out London:

This neighbourhood festival continues to grow and in it’s third year boasts historical walking tours, guided bike rides (and free advice from Dr Bike), a dog show, a local talent competition and communal maypole dancing, as well as workshops, facepainting and a tennis tournament for children, all taking place between 11am and 5pm in Tanner Street Park and Bermondsey Street. Delfina cafe and gallery space will host an exhibition of work by local artists and there are theatre tours and a garden party at Shunt Vaults. In Bermondsey Square, from 1pm to10pm, attractions include a programme of live music, The Comedy Club Live (courtesy of B2 Hotel) and free films at the 50-seater Shortwave Cinema.

Also on the calendar, not free but not crazy expensive either, is the Colourscape Music Festival. Time Out London has this to say:

This huge inflatable structure consists of almost 100 brightly coloured chambers radiating from a cathedral-like performance space. Visitors don coloured capes to wander around the labyrinth and at weekends musicians perform throughout the structure, providing an experience that is a fusion of colour and sound. Colourscape celebrates its twentieth anniversary this year.

Prices for this one are £7 for adults and £3.50 for children. Hours are Mon-Fri 12noon-1pm; Sat, Sun 1-6pm.