All week
DISCOVER CROSSRAIL: RIBA hosts an exhibition of designs for the Elizabeth line stations which open in 2018. See how they're going to look at this Platform For Design exhibition. Free, just turn up, 10am-5pm (Tuesday until 8pm)
FREE ART: Former Turner Prize nominee George Shaw reveals the results of his two-year National Gallery residency as Associate Artist. Renowned for his highly detailed approach, Shaw alludes to the theme of woodland in My Back To Nature, in his own imitable style — using his medium of Humbrol enamel, more commonly used to colour model aeroplanes. Free, just turn up, 10am-6pm
ASTRONOMY PHOTOGRAPHY: The night sky is one beautiful place and this Royal Observatory photo exhibition is a chance to see its most photographic side. Be amazed by images from the Astronomy Photographer Of The Year 2015, including the captivating winner, Eclipse Totality Over Sassendalen. Free, just turn up, 10am-5pm
Monday 6 June
ICY HEART: Asia House welcomes the work of Japanese artist Mieko Meguro. Xavier Heart/Icy Heart is an installation that reflects on the duality of the heart, with barbed wire and felt fabric. Free, just turn up, 10am-6pm
COMEDY: Seann Walsh and Kerry Goldliman preview their Edinburgh shows at the Amersham Arms for Happy Mondays comedy. £5, prebook, 8pm
Tuesday 7 June
FACE THE FEAR: Actor and academic Bella Merlin reveals the stories behind her new book, Facing the Fear: An Actor's Guide to Overcoming Stage Fright, at the Dorfman Theatre. Joined by both a neuroscientist and director, Merlin explores what actually happens when actors forget their lines. £5, prebook, 5.30pm
CHARTERHOUSE SQUARE: Take a sneaky peek behind the historic Charterhouse, dating back to 1347. The English country garden features roses, herbaceous borders, ancient mulberry trees and a small pond. Various garden herbs found here are still used in the kitchen today. £5, just turn up, 6pm
CANDLELIGHT AT THE MUSEUM: Discover the secrets of Sir John Soane's Museum on this candlelight tour through the exhibits. It's a magical look at the extraordinary house of one of Britain's greatest architects. Free, just turn up, 6pm (but get in the queue by 5.30pm, it's extremely popular)
Wednesday 8 June
WALK FITZROVIA: As part of FitzFest, walk through the "notable and quotable" bits of Fitzrovia with Camden Tour Guides Association. As part of the festival itself, there will also be a full live music programme filling the city streets with sound. Free, prebook, 11am-12.30pm (walk)
FIT FOR FREE: Get fit in Finsbury Park while playing with Highbury Korfball Club. Even if you've never played before, everyone's welcome at this friendly club. Meet at the Manor House entrance and get stuck in. Free, just turn up, 7pm-9pm, every Wednesday in June and July
BREW UP A STORM: Join Professor Joanna Haigh for an evening exploring our earth’s changing climate at Canalside Steps. Make your own cyanotype print, observe the sun through solar telescopes and discover why our climate is changing and how physics can help to predict our planet’s future. Free, prebook, 6.30pm
Thursday 9 June
SLIP INTO THE SHADOWS: Award-winning Pakistani artist Imran Qureshi has teamed up with Barbican for his latest work. Where the Shadows Are So Deep is a series of exquisite miniature paintings, hung at various heights in the dramatic 90m space of The Curve. Free, just turn up, 11am-8pm
MARX MEMORIAL LIBRARY: Take a behind-the-banner view of Marxism on this guided tour of the Marx Memorial Library. Visit Lenin's working space, original banners, posters and ceramics — even go underground and visit the cellars. £5/ £3, prebook, 1pm
RUSH HOUR MUSIC: For a tuneful interlude on your way home, head to St John's Waterloo where two-time Mercury Prize nominee Guy Barker joins Southbank Sinfonia, blending classical, jazz, blues and a whole load of history into a tale full of wit, mystery and theatricality. Free, just turn up, 6pm
Friday 10 June
PROJECT AWESOME: See great views of the city on your workout with Project Awesome at Primrose Hill. See the sun rise with this friendly fitness class. Free, just turn up, 6.30am
WELCOME BOATS: Take a seat on a Welcome Boat at Southbank Centre — it's teamed up with Pod Collective to signal messages of welcome to all refugees, as part of Refugee Week. Climb aboard and read the messages from people all over the UK. Free, just turn up, 10am-11pm
BRITAIN'S FIRST 11,000 YEARS: With EU voting just around the corner, discover more about Britain's special relationship with Europe at the British Museum today. From its earliest civilisations through 11,000 years of development, Professor Sir Barry Cunliffe provides an archaeological account of the British Isles. £5/£3, prebook, 6.30pm
COMEDY BIN: Free entry, non-stop laughter — it's no rubbish deal at Comedy Bin. Finsbury Park's finest funny folk on offer tonight include Jo Dexter, Sean Sellers, Sasha Ellen and more. Free, just turn up, 8pm
DELUXE: Six friends, moustaches and some crazy costumes — Deluxe explodes into Rich Mix tonight with a sound somewhere between electro, hip-hop, funk, soul and pop, and choreography that is as eccentric as it is contagious. Free, just turn up, 9.45pm
Saturday 11 June
QUEEN'S BIRTHDAY: To mark Liz's official birthday, a procession of motorised vessels will parade from Tower Bridge to Westminster Bridge — and back again. Grab your Union Jack and start waving from the riverside. Gets us all patriotic just thinking about it. Free, just turn up, 11am-1pm
FAMILY FITNESS: Jump your way into Saturday with this free family fitness class in Holland Park. The class is influenced by Brazilian culture (samba, batocada, capoeira) and kids are welcome too. Free, register, 11am-12pm
HIGHGATE FAIR: Join the fair in the square at Highgate Pond Square, a family-friendly afternoon of music, stalls, activities and entertainment. There are even fairground rides and Punch and Judy for a full-on summer feeling. Free, just turn up, 12.30pm-5.30pm
BARKING FOLK: For some fine folk music, head to Barking Abbey Ruins for a huge selection of artists from Badly Drawn Boy and Seth Lakeman, to 3 Daft Monkeys, Ella and the Blisters and more. Free, prebook, 5pm-9pm, until Sunday 12 June
Sunday 12 June
FARMERS MARKET: Cramer Street will be crammed with fresh produce for Marylebone Farmers Market. Have your fill from 30-40 stalls, selling some of London's finest foodstuffs. We particularly like the sound of The Dusty Knuckle Bakery. Free, just turn up, 10am-2pm
PARKLAND WALK: Go north and take the Parkland Walk South from Finsbury Park to Highgate. It follows the course of the old railway line and is packed with plants, trees and tiny creatures. Discover its history from the maps along the route or just enjoy the shady cool of the flora. Free, just turn up, all day
£5 YOGA: Bring out your best downward dog with Brixton Yoga. If it's your first class, you pay just a fiver for this class at Dogstar — that's your Sunday relaxation sorted. £5 (for first timers, £7 for return visitors), prebook, 7pm
