Friday: Drop by the Station Sessions at St Pancras for new music talent from 6-7pm.
Saturday: Head for Regent's Canal this weekend for the free floating fun at Shoreditch Festival (and Sunday).
Artists and makers in north Islington showcase their work for Islington Exhibits this weekend. One focal point is The Old Fire Station, Holloway N7, open 10am-8pm for exhibitions, installations, film screenings, performances and workshops - mostly free.
Make your way to Brockwell Park for the mad mix of rural fair and urban festival at Lambeth Country Show (and Sunday).
Rich Mix host 12 hours of Shubbak celebrations from midday, showing 20 top quality films from the Arab world plus live music, art and percussion workshops. Free before 7pm, £5 after.
Rummage in the jumble at New Gallery, Peckham SE15 between 1-6pm.
Drop by the Wonderful Walworth Garden Party between 12-4pm in Pembroke Community Garden, SE17.
Get in on the Zero Carbon Beach Party on the Thames from 7.30pm.
Sunday: Check out the hearse of the year show, vintage limos, stonemasonry, behind the scenes at the crematorium and Victoriana at Lambeth Cemetery Open Day, Blackshaw Rd, Tooting SW17 0BY between 10.30am-4pm, free.
Watch the open water swim in the river at Hampton Court from 9am.
Play games with Sandpit all afternoon at the National Maritime Museum, Greenwich to celebrate the opening of the Sammy Ofer Wing. Book yourself in at 12.30pm, free.
Monday: Quiz night at the Florist, Bethnal Green is just £1 entry and you could win the star prize of £20 (times are tough...) and the questions are "weird". 8pm start.
Tuesday: Prom it for the first of the Late Night Proms with a Schubert string quartet at 10pm. Prom tickets are just £5. Here's a link for tips on how to prom and our top 10 concert recommendations for 'Proms virgins'.
Wednesday: Fascinated by Google? This LSE public discussion takes you inside the Googleplex from 6.30pm in Hong Kong Theatre, Clement House, Houghton Street WC2.
Thursday: City of London Festival brings the Jive Aces to New Street Square for a free gig from 6pm.