All week
BONDS: The inaugural exhibition of new Somerset House space Gallery 31 closes this week. BONDS is a group exhibition by artists working out of Somerset House Studios, exploring the idea of connection beyond the physical and the immediate. Somerset House, free, just turn up, until 12 January
REMBRANDT #NOFILTER: Last chance to see Rembrandt #NoFilter, a free display marking 350 years since Rembrandt's death. The exhibition explores the artist’s celebrated Self-Portrait with Two Circles, which resides at Kenwood. A digital artwork, generated through visitors’ selfies, is created on-site too. Kenwood House (Hampstead Heath), free, just turn up, until 12 January
ARCHIE PRENTICE: Lauderdale House launches a new, free exhibition of paintings by figurative colourist Archie Prentice. More than 40 of his works go on show, mainly consisting of landscapes covering Britain, France, Italy, Greece and Morocco. Lauderdale House (Highgate), free entry, just turn up, 8 January-3 February
Monday 6 January
MOTIVATIONAL MOTIFS: Flagging on your new year's resolution already? Create your own motivational motif wall hanging to take home at this crafty evening — aided along by a drink or two from the bar, of course. All materials are provided. Drink, Shop & Do (King's Cross), £5, book ahead, from 6pm
UKULELE JAM: Every Monday, Queen of Hoxton holds a ukulele jam, open to anyone who wants to have a go on the instrument. Never played before? Borrow a uke for the night and get stuck in, strumming and singing along to well-known pop songs. Queen of Hoxton, free entry, just turn up, 7pm
MONDAY NIGHT MUSIC: Grab a seat at Wilton's Mahogany Bar for a free evening of live music by JB's Casual Vices. The New Orleans-inspired band plays a mix of jazz standards, jukebox R&B, mellifluous country songs and Jamaican rocksteady. Wilton's Music Hall (Limehouse), free entry, just turn up, 7.30pm-9pm
PUB(E) QUIZ: The Vagina Museum kicks off its 2020 programme with the regular Pub(e) Quiz. The vagina-themed trivia test is a chance to win prizes unlike those given out at your regular pub quiz. Vagina Museum (Camden Market), £3, book ahead, 7.30pm-9.30pm
Tuesday 7 January
CAN MATHS SAVE WHALES?: Saving the whales and curing cancer are two of the great challenges faced by science today. Professor Chris Budd gives a talk about the role that maths has to play in addressing both of them — in particular, how mathematical modelling can be used to learn how the world works, and how we can change it. Museum of London, free, just turn up, 1pm-2pm
JOURNEY TO THE MAYFLOWER: History author Stephen Tomkins gives a talk about how The Mayflower came to be launched, in a year marking the 400th anniversary of its voyage to America, Tomkins reveals a side of the story that not many people have heard before, linked to a period of religious unrest. Southwark Cathedral, £3, book ahead, 7pm-8.30pm
CAMILLE IN OCTOBER: Celebrate the life and works of working-class French lesbian author Mireille Best, who deserves more recognition for her contributions to LGBTQ+ fiction. Hear a talk and readings by translator Dr Stephanie Schechner, celebrating Best's novel Camille in October, published in 1988 and now available in English for the first time. Gay's The Word (Bloomsbury), free, just turn up, 7pm-8.30pm
Wednesday 8 January
HAWKSMOOR: London Metropolitan Archives' book group focuses on Hawksmoor by Peter Ackroyd this month. Join the group to discuss the 1985 novel, which weaves together modern and 17th century London. There's also a chance to view archive material relating to the book. London Metropolitan Archives (Clerkenwell), free, book ahead, 6pm-7.30pm
SWISH AND STYLE: Refresh your wardrobe without spending any money — and help the environment at the Swish & Style event. Take along some clothes (up to 15 items) that you no longer wear, in good, clean condition, and swap them for someone else's donations. You can also attend workshops to help you upcycle and salvage your existing clothes. Covent Garden Dragon Hall Trust, free entry, just turn up, 6pm-9pm
THE GREAT NORSE RUN: Danny Bent showcases his film The Great Norse Run as part of the Adventure Travel Film Festival. It tells the story of a run he led, from the north of Iceland to the south of the country, with 18 strangers joining him on the challenging adventure. London Film School (Covent Garden), £5, book ahead, 7pm-9pm
Thursday 9 January
PERSPECTIVE TOUR: Liz O’Riordan, a consultant breast surgeon who was diagnosed with breast cancer in 2015, gives a tour of the current Misbehaving Bodies exhibition. She offers her own perspective of topics covered in the exhibition, based on her personal and professional experiences. Wellcome Collection (Euston), free, just turn up, 6pm-6.45pm
WHAT'S WRONG WITH ART?: Londonist's own Visual Arts Editor Tabish Khan takes part in an evening of conversation looking at what's wrong with art. He and a panel of other experts discuss what can be improved in the visual arts industry, and what doesn't work in the arts world. Rich Mix (Shoreditch), free, book ahead, 6.30pm
ANIMAL FOLKLORE: South East London Folklore Society focuses on the folklore of animals for its January event. Find out how the beliefs of our ancestors have been passed down through civilisations and religions through history. The Old King's Head (Borough), £5/£3, book ahead, 8pm
Friday 10 January
THE MOUNTBATTENS: Biographer Andrew Lownie talks about the subject of his new book, The Mountbattens: Their Lives and Loves. He covers some of the more controversial episodes in the lives of former Chief of the Defence Staff Louis Mountbatten, and heiress turned humanitarian Edwina. A treat for fans of The Crown, season 3. National Army Museum (Chelsea), free, book ahead, 11.30am
LONDON MARI LWYD: Unless you're Welsh, it's unlikely that you've heard of the London Mari Lwyd... we hadn't but now we're intrigued. Everyone, Welsh or otherwise, is invited to join in, following a decorated horse's skull, visiting pubs and performing songs to celebrate the new year. London Welsh Centre (Gray's Inn Road), free, just turn up, 6.30pm
LIVE COMEDY: Robin Morgan is getting in early on this year's Edinburgh preview shows. The comedian tries out an hour of new jokes, leaving you to decide what they're worth. The Taproom (Islington), free (pay what you want at the end), book ahead, 6.30pm
Saturday 11 January
FAMILY STORYTELLING: Into the night is the theme of storyteller Olivia Armstrong's free event. Hear stories of magic and musicians, dancers and danger, performers and princesses, inspired by the current cabaret exhibition. Barbican, free, book ahead, 11am/2pm
CREATURE CREATIONS: The Grant Museum of Zoology has some weird and wonderful objects in its collections (trust us — we've had a good look). Take the kids along to a free craft afternoon where they can invent their own new animal based on what they can see in the museum. Grant Museum of Zoology, free, just turn up, 1pm-4pm
20 YEARS OUT: 20 years ago, the ban on homosexuality in the Armed Forces was lifted. To mark the occasion, National Army Museum hosts an afternoon of talks and tours where soldiers can share their own experiences from the last two decades, and how far the Army has come since. National Army Museum (Chelsea), free, just turn up, 2.30pm
Sunday 12 January
POEMS FROM AMERICA: Celebrate the 200th anniversary of George Keats — younger brother of poet John Keats — visiting from America. Keats House hosts an afternoon of poems which have crossed the Atlantic, to mark the anniversary of the visit by the Kentucky-based civil leader. Keats House (Hampstead), free, book ahead, 2pm-3pm
NO TROUSERS TUBE RIDE: Pretty much what it says, the British version of the 'No Pants Subway Ride' sees participants ride on the tube without their trews (note: despite the American name of the event, your undercrackers ARE required). The No Trousers Tube Ride puts groups of people onto various tube trains, acting completely nonchalantly except for their lack of leg covering. It's a lighthearted, fun event. Don't be the one who makes it weird by turning up in a mankini. Leicester Square, free, just turn up, 3pm
BAWDY BRITAIN: Presented as a rude musical history of the British Isles, Bawdy Britain is a journey round the country through time via the medium of song. Expect plenty of rudeness and double entendres. Round Table (Leicester Square), free, book ahead, 9pm-10pm