All weekend
CIRCUS: NoFit State Circus brings its show, Lexicon, to London for a two-week run. Expect a blend of impressive acrobatics, flame juggling, rope and trapeze acts and physical poetry performances, all to a soundtrack of a live band. Roundhouse (Camden), £15, book ahead, 3-18 January
WOOLLY JUMPERS: The Cutty Sark harks back to its wool-carrying missions between the UK and Australia with a family-friendly weekend of woolly activities. Cutty Sark, included in admission, just turn up, 4-5 January
FLEA MARKET: Start the new year by sprucing up your pad, with a little help from Hackney Flea Market. Over 30 vintage traders gather to sell their wares, ranging from furniture to homewares to records and bric-a-brac. Abney Public Hall, free entry, just turn up, 4-5 January
DARTS CHAMPIONSHIPS: After a lively stint at Ally Pally, the darts world heads east for the BDO World Professional Darts Championships, the first time the competition has been played at The O2. Watch 40 men and 16 women compete for the coveted title over the week, with the youth championship also taking place. Indigo at The O2 (North Greenwich), from £36, book ahead, 4-12 January
THE SNOWMAN: It's your last chance to see 12 festive interpretations of Raymond Briggs's The Snowman before they melt away. Each of the giant frosty fellows has been designed to represent one of the 12 days of Christmas, and the trail is completely free to follow — ideal if cash is a bit short after the festivities. London Bridge City, free, just turn up, until 5 January
LAST CHANCE EXHIBITIONS: It's the final weekend for several exhibitions, so see this lot while you can: The Moon at National Maritime Museum | Hogarth: Place and Progress at Sir John Soane's Museum | Science Photographer of the Year at Science Museum | Gingerbread City at Somerset House | Mary Sibande: I Came Apart At The Seams at Somerset House | Culture Under Attack at Imperial War Museum | London Is Love at Southbank Centre | Two Last Nights! Show Business In Georgian Britain at The Foundling Museum | War Brides at RAF Museum
Saturday 4 January
MR HARRIS'S BOOK: Ever heard of Mr Harris's Book? It was a list that named the ladies who worked the streets of Georgian London. Find out more about it on this guided walk through Covent Garden, visiting some of the buildings they frequented to make a living. Strand, £12/£9, book ahead, 11am-1pm
EXPLORE ZOOLOGY: Take the kids along to the excellent Grant Museum of Zoology, and get hands-on with some of the artefacts which are normally kept behind glass. Handle the objects, and ask the experts your questions. Grant Museum of Zoology, free, just turn up, 1pm-5pm
ARCHITECTURE TOURS: Get a closer look at the National Theatre, on one of its regular architecture tours. See both inside and outside the building, a Brutalist structure whose appearance regularly splits opinion, National Theatre, £15, book ahead, 2.30pm
MOTHER OF THE BRONTËS: Hear the story of Maria Branwell, later Maria Brontë, mother of literary siblings Charlotte, Emily and Anne. Author Sharon Wright, who has just written a book on the topic, recounts the unlikely meeting between Cornish gentlewoman Maria and poor Irish curate Patrick Brontë. Southwark Cathedral, £7, book ahead, 2.30pm-4pm
COMEDY: Comedy evening Swipe Right offers a show of improv and stand-up comedy, with prizes to be won. Kayleigh Cassidy, Do The Right Scene and Dingbats Improv are among the acts performing, and there's also a music quiz to take part in. The Miller (London Bridge), free, book ahead, 7.30pm-10.30pm
CLUB CLASSICS: If you didn't do enough dancing on New Year's Eve, head east for an evening of house, disco and club classics, doubling up as a high-intensity cardio session split across two floors. Queen of Hoxton, £5/free, book ahead, 8pm-2am
Sunday 5 January
SING IN 2020: Join secular community Sunday Assembly to sing in the new year. Intended as an alternative to religious gatherings, take part in a sing-song that eschews hymns for pop and rock tunes, accompanied by a live band. As well as marking the new year, the events celebrates Sunday Assembly's seventh birthday, so stick around for tea and cake at the end. Conway Hall (Holborn), suggested donation £10, just turn up, 11am-1pm
SHERLOCK HOLMES: Fictional detective Sherlock Holmes is associated with the area around Baker Street, but this Footprints of London guided walk turns to east London instead. You don't have to have read any of the books to enjoy it — though it would help if you have — as you take a closer look at some of Holmes's mysteries. Royal Exchange (Bank), £12/£9, book ahead, 11am-12.30pm
PALACE TOUR: Learn about the history of Fulham Palace on this guided tour. It was home to the Bishops of London for over 1300 years, and the tour is a chance to learn how individual occupants left their mark on the building and grounds. Fulham Palace, £6, just turn up, 12.30pm-1.30pm
DÍA DE LOS REYES: Mark Día de los Reyes (Day of the Kings, Mexico's version of Epiphany) at a family activity session. Learn what does into a traditional bread called Rosca de los Reyes, then make your own to take home. Museum of London, free, book tickets on arrival, 12.30pm/1.45pm/3pm
PAINT WINTER: Unleash your inner artist at Pop-Up Painting's Paint Winter + Wine event. All art supplies are provided, and no experience is necessary as you create your own version of Felix Vallotton ‘s Snowy Landscape. A glass of wine is included, and further refreshment is available from the bar. The Horniman at Hays (London Bridge), £31.99, book ahead, 2pm-4pm
TWELFTH NIGHT: London's annual Twelfth Night celebrations mix ancient customs with modern festivities, making for a bizarre and eclectic event. Head to the riverside near Shakespeare's Globe to witness wassailing, The Holly Man (or Green Man) being paraded across the river, dramatic performances, and a chance to be crowned King or Queen for the day by finding a bean or a pea in a cake. An odd (but fascinating) one. Bankside, free, just turn up, 2pm
VAMPIRES IN HACKNEY: Join London Dreamtime for an adults-only storytelling session themed on vampires. Not for the faint-hearted, it's an afternoon of tales of vampires of Old Russia, blended with live music, and finished up with a bar to steady your nerves. Age 18+. Folklore (Hackney Road), £5, book ahead, 3pm
