All week
ARCHIE PRENTICE: Last chance to see this free exhibition of paintings by figurative colourist Archie Prentice. More than 40 of his works are on show, mainly consisting of landscapes covering Britain, France, Italy, Greece and Morocco. Lauderdale House (Highgate), free entry, just turn up, until 3 February
THE LOST GIRL: DH Lawrence's book of the same name is the basis for The Lost Girl, a film-based installation by artist Kate McMillan. It's set in the future, at a time when society as we know it has been decimated, and follows a cave-dwelling girl on the English coast. Bush House (Strand), free, just turn up, until 28 February
SOCIAL REVOLUTION: Women's liberation and gay liberation in the 1970s-80s is the subject of a free exhibition, marking 50 years since both the first women’s liberation conference in Oxford, and the first UK meeting of the Gay Liberation Front at LSE. Archive material shows how thousands of people were mobilised to change the world through speaking out. LSE Library (Holborn), free, just turn up, until 3 April
MUSHROOMS: The common — and not so common — fungus is the subject of a new Somerset House exhibition. Mushrooms: The art, design and future of fungi contains the work of over 40 artists and musicians, celebrating all aspects of mushrooms, from their psychedelic legacy to their practical use in creating sustainable textiles. Somerset House, free, just turn up, 30 January-26 April
Monday 27 January
BREXIT IMPLICATIONS: Hear a panel of experts discuss the implications of Brexit on the UK economy. Find out what the forecasts are for different sectors once the UK leaves the EU, and how accurate these forecasts are likely to be. LSE (Holborn), free, just turn up, 6.30pm-8pm
THE VOLUNTEER: Jack Fairweather, author of The Volunteer, tells the true story of a Polish resistance fighter who infiltrated Auschwitz. The event marks Holocaust Memorial Day, and goes into how Witold Pilecki worked to uncover the atrocities of Auschwitz. National Army Museum (Chelsea), free, book ahead, 6.30pm
ALL THAT SCRATCH: Attend a live recording of musical theatre podcast All That Scratch. The hour-long show is a chance for new writers to showcase their work, and to tell the stories behind it in interviews. The Other Palace (Victoria), £5, book ahead, 7pm
COMEDY: Award-winning comedian Laura Davis offers an hour of her newest work as she hones it for her upcoming shows. We don't yet know what it's about, but for a fiver, why not give it a go? Pleasance Theatre (Islington), £5, book ahead, 7.45pm
Tuesday 28 January
PROHIBITION: Professor of American History, Gary Gerstle, gives a free lecture about Prohibition in America. Find out how the banning of alcohol created a culture war, splitting the country several ways: between the native-born (white Protestants) and foreign-born (Catholics and Jews), between religion and science, and between the country and the city. Museum of London, free, just turn up, 6pm-7pm
KUBRICK'S WORLD: Learn about the element of surprise in Stanley Kubrick's films, in a lecture and exhibition of objects from Dr. Strangelove to 2001: A Space Odyssey and Eyes Wide Shut London. Expert Carl Grinter talks about the film design, production and reception of Kubrick’s work. College of Communication (Elephant & Castle), free, book ahead, 6.30pm-8pm
Wednesday 29 January
MUSEUM LATES: Science Museum keeps its doors open late on the last Wednesday of every month, for an evening of adults-only activities. Browse the displays and exhibitions after hours, or take part in activities relating to this month's theme, medicine. Discuss the history and horrors of the humble condom, listen to songs performed by the NHS choir, or have a dance at the silent disco. Science Museum (South Kensington), free, book ahead, 6.45pm-10pm
EUROPEANS: Ahead of the UK leaving the EU, the latest European put in the spotlight at Dash Cafe is French photographer, painter and poet Dora Maar — the subject of a current Tate Modern exhibition. Hear from curators, and fellow poets and artists about the Surrealist's career, and the photomontages she became known for. Rich Mix (Shoreditch), £5, book ahead, 7pm
POLARI: Novelist and critic Paul Bailey is the special guest at this month's edition of LGBTQ+ literary salon Polari. He reads from his first poetry collection, Inheritance, with other authors Nathan Evans, Jill Gardiner, John O’Connell, and SJI Holliday also on the line-up. Southbank Centre, £5, book ahead, 7.30pm
Thursday 30 January
KING CHARLES I CEREMONY: The anniversary of the death of King Charles I — who died by execution in 1649 — is marked in a special ceremony by the Society of King Charles The Martyr. It takes place at Banqueting House, the site of the execution, with wreath-laying, prayers, and a religious sermon. Banqueting House (Whitehall), free to watch, just turn up, 11.40am
LIVE MUSIC: Do something different with your lunch break, and enjoy a free concert. Chamber musicians The Galliard Ensemble perform four pieces in a free concert at LSE's Shaw Library. LSE (Holborn), free, just turn up, 1.05pm-2pm
DIGGING UP MLITON: Writer Jennifer Wallace talks about her darkly humorous novel, Digging Up Milton. It's set in 1790, over a century after the death of poet John Milton, and involves his bones, a gravedigger, a lock of hair, and John Keats. Keats House (Hampstead), £4.50, book ahead, 6.30pm-8pm
Friday 31 January
PRISONERS OF WAR: The National Archives is running a volunteer project to catalogue its surviving collection of second world war German record cards of British and Commonwealth prisoners of war and some civilian internees. Find out more about the project, and see some of the documents involved, at this drop-in session. National Archives (Kew), free, book ahead, 2pm-4pm
NATURAL HISTORY LATE: Dinosaurs is the theme of this month's Friday late at Natural History Museum — and it's a theme we heartily approve of. Scientists are on hand to talk about how dinosaurs lived, and share an insight into dino research going on at the museum, plus there's a bar, science demos and other activities. Natural History Museum (South Kensington), free, just turn up, 6pm-10pm
WOMEN OF SOUL: Celebrate the likes of Aretha Franklin, Tina Turner and Etta James, at an evening dedicated to the women of soul. A female-fronted house band performs live, interspersed with soul, funk, rock 'n' roll sets from DJs. Blues Kitchen (Camden), £4.52, book ahead, 9pm-2am
Saturday 1 February
CHINESE NEW YEAR: The Chinese New Year celebrations continue at Brent Cross, where there's a day of free, family-friendly activities. Watch traditional lion and dragon dances, and Tai Chi demos, take part in arts and crafts, have your name written in Chinese calligraphy, and let the kids get their faces painted. Brent Cross Shopping Centre, free, just turn up, all day
CRAFT MARKET: Crafty Fox's latest market is even more of a bargain, as it's a sample and seconds sale. Traders specialising in ceramics, jewellery, textiles and more sell ofF their wares at reduced prices — either one-off samples, slight seconds, or end of line items. Mercato Metropolitano (Elephant & Castle), free entry, just turn up, 11am-5pm
FIX FILM NIGHT: Ahead of upcoming play The Fix, Pleasance Theatre screens a series of East Asian horror films, and tonight it’s the turn of Audition. The 2005 Japanese film is about a man who decides to remarry following the death of his wife, and holds auditions for a new spouse, meeting someone who isn't all she seems. Pleasance Theatre (Islington), £4.50/£3, book ahead, 9.30pm
Sunday 2 February
CROYDON AIRPORT: The monthly opening of the Croydon Airport Visitor Centre is a chance to explore the micro-museum about the airport, and get inside the world's oldest air traffic control tower. Learn about the history of the airport, from first world war airfield, to London’s international airport, Battle of Britain airfield and closure in 1959. Croydon Airport, free (donations welcome), just turn up, 11am-4pm
VINTAGE FASHION: Restock your wardrobe and get some fashion inspo at The Vintage Collections, a vintage fashion fair with over 50 traders selling clothes, jewellery, accessories and more. Items date from the Victorian era through to the 1990s (yeah, we can't believe the 90s now count as 'vintage' either). Freemasons Hall (Covent Garden), £5, book ahead, 11am-5pm
FRIENDS AND LOVERS: Comedian Lou Sanders headlines and hosts a night of new and old comedy, by new and old comedians. The Bill Murray (Islington), £5, book ahead, 6pm-8pm
