Monday: Get your head around Imagining the Internet: policy challenges at London School of Economics from 6.30pm (free).
Tuesday: Watch An unnatural history of London at East Reservoir, Stoke Newington and see the fox family make their film debut 6.30pm (free, please book).
Wednesday: If you've ever wanted try Life Drawing try it for free tonight in Bermondsey from 6.30pm (free first go).
Thursday: Catch an intimate performance of Nic Green: Slowlo, a poetic response to a year spent living in a remote place, at Toynbee Studios at 5.30, 6.30 and 9pm (tickets £5).
The RNIB Literary Wonderland opens at Cathedral Square 9am-6pm (free).
Friday: Be at the special screening of London - The Modern Babylon at Rough Trade East from 6.30pm (free, no wristband).
Saturday: Find fantastical pianos, squishy bells, walks, talks, dance performance, exhibitions, music, art, maths and more at Bloomsbury Festival from Friday to Sunday (free - pre-book some events).
It's the annual Home Movie Day at the Cinema Museum, Kennington with a film clinic to help with your old films, cake and a special screening of Hitchcock's home moves from 1pm (free).
Sunday: It's Apple Day at Spitalfields City Farm, Forty Hall Farm in Enfield and at Green Peppers Orchard and Forest Garden in Camden — take your pick!
Check out our things to do in London for free page for more.
Photo of Bloomsbury Festival 2010 by McTumshie via the Londonist Flickrpool.