Monday: Exhibition Road Show has free entertainment all week. This evening there's a silent disco, music from the Olympianist, a capella group Sense of Sound and the Royal College of Music, plus acrobatic feats from the Exhibitionists, a hand crafted particle accelerator and vintage board games from 6-10pm (free).
The Watch This Space festival continues outside the National Theatre with circus and theatre for all the family (free).
Tuesday: Last Tuesday at RIBA, Portland Place is all about Celebration and Spectacle with talks, film, exhibitions, live music and London 2012 screening live 6-10pm (free).
Kino London returns to the Horse Hospital, Russell Square for an evening of short films, filmmaking activies and free popcorn from 8.15pm (£4 entry, £3 with flyer)
Science London does origami dinosaurs at Drink, Shop, Do from 7pm (free).
Thursday: It's International Music Week at Wilton's so drop by the Mahogany bar any night for the Global Beats Festival. Tonight it's Baba Adesose Wallace from Nigeria 7-11pm (free).
Friday: Pop into County Hall where Japan says thank you with an open house, Arigato in London open daily all week till Sunday (free).
Africa Fashion Week comes to Spitalfields Market for two days (ie not a week) of catwalk shows and designer exhibitions (free entry but register for shows).
Saturday: Watch the Olympic Men's 20km Race Walk from 5pm (free).
Go to the Fish Island Festival at iCAN Studios on every day of the Olympic Games, with big screens, big BBQ, games, face painting, arts and crafts and the Bicycle Library daily, 10am-10pm (free).
Sunday: Cheer on the Olympic Women's Marathon on the streets of London from 11am (free).
It's Wild Bird Week at the RAF Museum, Hendon with falconry displays on the helipad every day 30 July - 5 August, throughout the day (free).
Check out our things to do in London for free page for more.