All week
SECRET RIVERS: The secrets of London's historic waterways are revealed in a major new exhibition at Museum of London Docklands. Secret Rivers brings together art, photography and archaeology to tell the stories of the capital's rivers, streams and brooks, many of which have been lost over time. Museum of London Docklands, free, just turn up, 24 May-27 October
HALF TERM: School holidays don't need to be expensive. See our guide to things to do in London in half term for ideas to keep kids occupied, whatever your budget. Until 2 June
WILDLIFE ART: Animal lovers are in for a treat at the Wildlife Artist of the Year exhibition, where all artworks are for sale in aid of the David Shepherd Wildlife Foundation. Paintings, drawings, sketches and sculptures of several different species are featured. We've been in the past and have never managed to leave without buying something, but you're welcome to just browse too. Mall Galleries, free, just turn up, 29 May-2 June
LONDON RIVERS WEEK: Celebrate the waterways that flow through our capital at London Rivers Week. Organised by Thames21, the festival aims to get Londoners interested in and caring for London's lesser-known rivers through guided walks, science demonstrations and real-life research. Various locations and prices, book ahead, 25 May-2 June
WANDSWORTH HERITAGE FESTIVAL: Guided walks, illustrated talks and exhibitions are some of the events at Wandsworth Heritage Festival, several of which are free. Highlights include an exhibition about Battersea Power Station, a guided walk of Balham Hill and family archaeology session. Full programme here. Various locations and prices, book ahead, 25 May- 9 June
Monday 27 May
ENGINE MUSEUM: The Markfield Beam Engine Museum is open to the public today, offering a chance to see inside the Grade 2 listed engine hall, and witness an 1888 restored steam-powered beam engine in action. Markfield Beam Engine & Museum (Tottenham), free (donations welcome), just turn up, 11am-5pm
Tuesday 28 May
SUPREME COURT: Go behind the scenes at the Supreme Court. See inside the courts and visit parts usually off-limits to the public, including the Library. An exhibition offers an insight into the history of the building, and what goes on in the courts, and staff are on hand to talk about working there. UK Supreme Court (Westminster), free, just turn up, 9.30am-4.30pm (repeated tomorrow)
MUSIC HALLS: As part of Wandsworth Heritage Festival, hear about the history of musical halls in the Battersea and Wandsworth areas, and how they improved the lives of local residents in Victorian and Edwardian times. Battersea Arts Centre, free, book ahead, 7pm
COMEDY: Nigel Ng tries out new comedy material, covering his life in the UK as a Malaysian immigrant, including topics such as cultural identity and Wagamama. Pleasance Theatre (Islington), £5, book ahead, 9pm
Wednesday 29 May
GOODNIGHT LONDON: Between the two weekends of festival madness, All Points East hosts four days of free events. Tonight there's an outdoor screening of Goodnight London, a film collage which looks at how the rapid pace of development is affecting creative communities. It includes a Q&A with the director, and a panel discussion about gentrification. Victoria Park, free, just turn up, 5.25pm-7.20pm
MATHS GETS MESSY: You may not be all that interested in maths... but what if we brought chocolate fountains into the equation? This year's Joint London Mathematical Society Annual Lecture looks at mathematical modelling of complex fluids, to answer questions such as why the chocolate in a fountain doesn't fall straight down. Museum of London, free, just turn up, 6pm-7pm
MUSEUM LATES: Science Museum stays open late for an adults-only evening themed around the digitisation of the kilogram. It's more thrilling than it sounds, with museum tours, cardiac science, a 'life golf course' and other activities, as well as a chance to see the museum's exhibits after hours. Science Museum (South Kensington), free, book ahead, 6.45pm-10pm
Thursday 30 May
SUMMER BY THE RIVER: While we're dubious about the name London Bridge City (given to the area between London Bridge and City Hall on the south bank of the river), we do admit that a jolly good party happens there every year. Summer By The River kicks off today, beginning a summer of free film and sport screenings, live music and other entertainment. London Bridge City, free, just turn up, from 30 May
VICTORIA AND ALBERT: Queen Victoria and Prince Albert are turning 200. Celebrate with a Victorian day in Hyde Park. Don a costume from the period and have a go at skipping, yo-yoing, hoop and stick, and other Victorian toys. Learn about how the royal couple influenced the development of Hyde Park and Kensington Gardens, and hear about Victoria's childhood in the area. Hyde Park, free, book ahead, 11am-3pm
EDUCATING LONDON: From late-Victorian elementary schools, to the new comprehensive schools of the 1950s, this illustrated talk covers the history of institutions created or maintained by the London County Council between 1889 and 1965. London Metropolitan Archives, free, book ahead, 2pm-3pm
Friday 31 May
LONDON HISTORY DAY: Today is London History Day, with events taking place around the capital to celebrate. London Metropolitan Archives has a programme of events for adults and kids, including talks and document displays (free, book ahead, 10.30am-4pm) and a celebration of the women who built Waterloo Bridge at LSE (free, just turn up, 2.30pm-5pm).
MUSEUM LATE: Natural History Museum keeps its doors open for the monthly museum late. The theme this time is how Earth has changed over time. Discover how our planet evolved over millions of years through talks from museum researchers and pop-up science stations. Otherwise, visit the usual displays and exhibitions after hours, or stay really late for the silent disco. Natural History Museum (South Kensington), free entry (charge for some events and exhibitions), just turn up, 6pm-10pm
SUMMER ON SCREEN: Wembley Park's free outdoor cinema, Summer On Screen, begins its season today with a Queen double-bill (that's Freddie and co., not the monarch). Bohemian Rhapsody is shown, followed by a screening of The Freddie Mercury Tribute Concert, held at Wembley Stadium in 1992. Wembley Park, free, just turn up, 7pm
Saturday 1 June
HENDON PAGEANT: The traditional Hendon Pageants — fundraising events held in the 1920s — are re-lived for the second consecutive year at the RAF Museum's aerodromes. A coconut shy and carousel form part of the vintage fairground, with live music, swing dancing, vintage clothes stalls, engine displays, food and drink stalls, and even a flypast. RAF Museum (Hendon), free, just turn up, 1-2 June
CAR RALLY: The London to Brighton Classic Car Run begins in Greenwich Park this morning, giving early risers a chance to glimpse the vintage vehicles before they set off on their journey to the coast. It's the warmer, more modern version of the event which takes place in November every year, and follows a scenic route down to Brighton. Greenwich Park, free to watch, just turn up, from 7am
ANNIE: If you're hoping that The Sun Will Come Out Tomorrow, head to this family film screening and singing workshop. Local children’s group Serlina’s Singing Glee Club run the musical course, which covers different singing techniques, before 1982 musical film Annie is screened. Harris Academy South Norwood, £5, book ahead, 1pm-3.20pm
Sunday 2 June
ANTIQUES ROADSHOW: BBC mainstay Antiques Roadshow films in south-west London today. Even if you haven't got any family heirlooms to show off, head along to have a nosey at what other people keep in their attics... and maybe even appear on TV. Morden Hall Park, free, just turn up, 9.30am-4.30pm
WEST NORWOOD FEAST: Once a month, a team of local volunteers put on the West Norwood Feast, a free entry street market with food and drink, craft and vintage stalls to browse, plus kids' activities, live entertainment and more. Norwood High Street, free, just turn up, 10am-4pm
DOG SHOW: Bring a dog, or don't bring a dog — the Gunnersbury Dog Show is open to everyone (expect cats, maybe). See dogs go head to head in different classes, browse stalls, and watch a Flyball demonstration. Gunnersbury Park, free entry, just turn up, 11am-5pm
