All week
WINTER LIGHTS: Free light festival Winter Lights returns to Canary Wharf, with more than 20 light installations and interactive light artworks dotted among the skyscrapers. Take a look at last year to get an idea of what to expect, and download this year's map to help you on your way. A variety of vintage food trucks are on hand to keep you fuelled. Canary Wharf, free, just turn up, 5pm-10pm, 15-26 January
PHOTOGRAPHY: Work by photographer Lucy Clive goes on display this week. The carefully-composed colour photos are all captured with her iPhone, and offer a closer look at seemingly ordinary everyday moments, showing the beauty in our daily surroundings that we normally miss. All images are for sale in editions of 12. 50 Golborne Road (Westbourne Park), free, just turn up, 14-19 January
ANATOMY OF MELANCHOLY: This new exhibition is based on a 17th century book of the same name, which offered up remedies for melancholy. Take a closer look at how the proposed causes and cures of melancholy are represented within the museum's own art collection. Bethlem Museum of the Mind (Beckenham), free, just turn up, 16 January-27 April
PORTRAIT OF JEREMY BENTHAM: This new 3D portrait of philosopher Jeremy Bentham was created using scans of his real head, and is designed so he seems to follow your movements around the room. For the full experience, make time to see the Jeremy Bentham auto-icon — on permanent display — while you're there. UCL, free, just turn up, 14 January-7 February
Monday 14 January
FREE DOUGHNUTS: To celebrate the launch of its new Hammersmith store, Crosstown Doughnuts is giving away free doughnuts. To bag a free raspberry jam or vegan coconut and lime dough bite, you need to be one of the first 100 customers of the day (store opens at 7.30am) and make any purchase to receive your freebie. Crosstown Hammersmith (1a Beadon Road), free, first come first served, first 100 customers every day, 14-16 January
BOARD GAMES: Spend a chilled out evening learning and playing new board games, at an evening hosted by screenwriter and board games fanatic Charlie Fish. Forget Monopoly and Scrabble, and learn how to play the likes of Ticket To Ride and King Of Tokyo. The Ritzy (Brixton), free, book ahead, 6.30pm-11pm
Tuesday 15 January
DEEP OCEAN: How true is the oft-quoted statement that scientists know more about Mars than our own ocean floors? Find out about recent developments in deep ocean exploration, the history of exploring, and the deep-sea discoveries which have changed the way we think about certain things. Museum of London, free, just turn up, 6pm-7pm
STADIUM REGENERATION: In recent years, Highbury, Stratford and Tottenham have all felt the effects of a new stadium being built in their midst (well, that last one's still ongoing...). But have they actually done anything to regenerate the local communities? Hear Mark Panton, from Birkbeck, University of London's Sport Business Centre, discuss his recent research in this area. City & Islington College (Finsbury Park), free, book ahead, 6pm-7.30pm
WAR: War has always been a part of human society, but what, if anything, can be done to make war less likely in future? Hear a philosopher, a historian and a cultural evolutionist discuss the topic at this free debate. LSE (Holborn), free, just turn up, 6.30pm-8pm
Wednesday 16 January
SOUNDSTATE: Southbank Centre hosts five-day festival Soundstate, celebrating artists making new music in the 21st century. Orchestras, sinfoniettas and solo artists from Iran, Turkey, Pakistan, Slovenia, Sweden, Germany and beyond all feature and many — although not all — of the performances are free. Southbank Centre, price and booking information varies by event, 16-20 January
VIDEO GAMES: Today's free V&A lunchtime lecture is about video games, focusing on how the technological advances of recent years have changed the way games are designed, discussed and played. It ties in with the museum's current videogames exhibition. V&A Museum (South Kensington), free, just turn up, 1pm-1.45pm
KNITTING KITTENS: Love cats? Spend an evening at Battersea knitting toys and blankets for the home's feline residents — or make something for your own pet. Bring your own wool and needles. Battersea Dogs & Cats Home, minimum suggested donation £2, just turn up, 5pm-8pm
JAWDANCE: Jawdance is a monthly poetry performance night where performers are invited to sign up for an open night slot and share their latest work. Sign up for a slot yourself (maximum three minutes) or just sit back and watch the performances. Rich Mix (Shoreditch), free, just turn up, 7.30pm
Thursday 17 January
IN THE DARK: Artist's collective The London Group hosts a three-day exhibition in the dark. Each work of art generates its own lights, so expect projections, illuminations and light boxes, with all surfaces — including the ceiling — used. Cello Factory (Waterloo), free, just turn up, 2pm-6pm, 17-19 January
SPACE TECHNOLOGY: Hear Dr Subhanjoy Mohanty talk about the latest scientific results from the Kepler Space Telescope, which is designed to detect other worlds. Find out what the telescope has shown us about the architecture of our own solar system, strange new kinds of planets, and if there could possibly be life on other planets. Imperial College (South Kensington), free, book ahead, 6.45pm-8pm
POEMS FOR THE NHS: Attend the launch of a new anthology of poems all about the NHS, celebrating 70 years of our health service. Poems from established and new poets are included in the book, which raises money for NHS Charities Together. The Poetry Café (Covent Garden), free, just turn up, 7pm-10.30pm
Friday 18 January
TRIAL OF CHARLES I: Hear the details of the trial of Charles I in 1649, in this talk and document display at the National Archives. Dr Neil Johnston covers the charges laid against the king, his attitude and conduct, and whether his execution was inevitable. National Archives (Kew), £5/£4, book ahead, 2pm-3pm
GUERILLA ART: Watch Guerilla Art, a documentary film about street art pioneers Futura, Rammellzee and Blek le Rat, and the early days of graffiti. The screening is followed by a Q&A with the film’s director, Sebastian Peiter. British Museum, £3/£2, book ahead, 6.30pm-8.15pm
FALKLANDS WAR: Lieutenant General Sir Cedric Delves and Helen Parr are in conversation with Major General Arthur Denaro about the Falklands War, and the experiences of those who fought there — Delves commanded an SAS squadron himself. National Army Museum (Chelsea), £5, book ahead, 6pm-8pm
BIG WRENCH: Watch a screening of Chris Burden's Big Wrench, an autobiographical film about the artist's relationship with a truck called Big Job. It's also a chance to see exhibition Chris Burden: Measured, after hours. Gagosian Gallery (King's Cross), free, book ahead, 6pm-8pm
COLLECTING CATS: New children's book Collecting Cats has a launch party tonight — a chance to get your feline fix if you couldn't make it to Battersea on Wednesday. Author Lorna Scobie is signing copies. Gosh Comics (Soho), free, just turn up, 7pm-9pm
Saturday 19 January
EXPLORE ZOOLOGY: Take the kids along to a family-friendly afternoon of zoological fun. The Grant Museum gets some of its specimens out of its cabinets and lets the public get hands-on with shark's teeth, pangolin scales and more. Grant Museum (Warren Street), free, just turn up, 1pm-4pm
STUDIO TOURS: Go behind the scenes at Somerset House and find out how one wing of the building has been transformed from former Inland Revenue offices into artists' studios. Somerset House (Strand), free, book from 10.30am on the day, 1.15pm/3.15pm
FAMILY STORYTELLING: Expert storyteller Vanessa Woolf recounts the tales of Daedalus & Icarus and The Freedom Bird at this family-friendly storytelling session, helped along with music and props. Leighton House Museum (Holland Park), £3, book ahead, 2pm-3.30pm
TATE LATE: Tate Modern keeps its doors open late for an intimate four-hour DJ set with special guest DJ Mumdance, who's worked with the likes of Skepta and Jammer. We recommend listening to his Fabric mix from a few years ago to get you in the mood. Tate Modern (Bankside), £5, book ahead, 7pm-11pm
Sunday 20 January
SWAP SHOP: Give your wardrobe a bit of a refresh by taking your old (but good condition) garments along and swapping them for other people's donations. Filming for a BBC3 documentary is taking place at the event, so you might even end up on the TV. Refettorio Felix (Kensington), £3, just turn up, 11am-3pm
SURVIVOR TALK: John Dobai experienced the Holocaust in Budapest in 1944, and survived thanks to Swedish diplomat Raoul Wallenberg. Dobai's story is recounted in forthcoming film The Donkey Field, and today he's in conversation with his filmmaker daughter Sarah. Jewish Museum (Camden), free, book ahead, 2pm-3pm
