All weekend

PARADOX MUSEUM: 50 interactive exhibits and 25 rooms make up the Paradox Museum, a new venue on Brompton Road in Knightsbridge. Reverse rooms, a giant kaleidoscope and a mirror maze are among the experiences, which are suitable for all ages. From 17 July

DINOSAUR GARDEN: Be among the first to see the Natural History Museum's new Evolution Garden — or 'Dinosaur Garden' — outside its main entrance, on its first weekend open to the public. Wend your way through sunken paths, along an immersive timeline of plants, geology, and representations of reptiles, birds and mammals. Oh, and it's home to a huge bronze cast of a dinosaur skeleton too. FREE, from 18 July

HYPER JAPAN FESTIVAL: Love all things Japanese? Get yourself to Hyper Japan, a celebration of Japanese culture at Olympia London this weekend. Live performances, a market, food and drink stalls and a sake experience are all part of the fun. 19-21 July

RIVER STAGE: The Rambert Dance Company curates this weekend's programme at the open-air (and free!) River Stage outside the National Theatre. Drop by throughout the weekend for dance performances and workshops including an excerpt from the Peaky Blinders stage adaptation. FREE, 19-21 July

BBC PROMS: This year's BBC Proms is now underway, with three events at the Royal Albert Hall this weekend. The BBC Concert Orchestra celebrates the Disco movement on Saturday night, followed by British choral groups The King's Singers and VOCES8 on Sunday morning, and a celebration of Sir Mark Elder's last season as Music Director after 25 years in the role on Sunday evening. For all your info on tickets, highlights, promming and the like, peruse our guide to the BBC Proms 2024. 19 July-14 September

FOOD FESTIVAL: Eat your way around the world at the National Geographic Traveller Food Festival, at the Business Design Centre in Islington. Hear from cookbook authors including Yui Miles and Denai Moore, and watch live cooking demos and masterclasses, so you can attempt to recreate your favourite dishes at home. 20-21 July

ICE WEEKEND: Once a year, the London Canal Museum in King's Cross holds an ice weekend, celebrating the space where ice was stored before the days of refrigeration. Descend by ladder into an Victorian ice well (Sunday only) and take part in all manner of ice-themed activities back above ground. 20-21 July

ENSEMBLE FESTIVAL: Ensemble, a free outdoor performance festival from Newham-based arts organisation Certain Blacks, takes place at Royal Victoria Docks all weekend. Among the performers are contemporary circus company NoFit State Circus, and Gorilla Circus, whose show combines acrobatics, street dance and roller skating, performed on a giant moving treadmill. Check out the full schedule. FREE, 20-21 July

HENRY VIII'S JOUST: Cheer on your favourite knight — or even a king — at Henry VIII's Joust at Hampton Court Palace. The recreation of a Tudor event from 1533 sees daredevil tricks performed on horseback, along with falconry displays and food and drink stalls. 20-21 July

LONDON E-PRIX: All-electric vehicles take over the area around Royal Docks and ExCeL for the London E-Prix all weekend. The track partially goes inside the ExCeL Centre itself, and there's a fan village, live music and kids' area for spectators. 20-21 July

THE LAST CARAVAGGIO: The National Gallery's display, The Last Caravaggio, showcases the last known work of Italian painter Michelangelo Merisi da Caravaggio. It's the first time The Martyrdom of Saint Ursula has been on display in London for 20 years — and this weekend is your last chance to see it. FREE, until 21 July

GREAT ESCAPES: Also closing this weekend is The National Archives' current exhibition, Great Escapes, about prisoners of war and civilians who were confined to internment camps during the second world war. Some managed to escape physically, while others remained trapped but found freedom in creative endeavours such as art and theatre productions, or in writing letters to loved ones. FREE, until 21 July

Saturday 20 July

ANTIQUES MARKET: Get up early and head to north-west London for the Wembley Park Antiques Market. Browse through antiques, collectables, vintage homeware, jewellery, furniture and more — all inside a covered car park, meaning you don't need to worry about the weather. 9am-3pm

CART MARKING CEREMONY: One of London's quirkier events is the Ceremony of Cart Marking, a 500+ year old tradition by the Worshipful Company of Carmen. See a collection of handcarts, horses and carts, steam-driven, electric, solar-powered and hydrogen vehicles on display at Guildhall, with Livery Masters and Court Assistants in their official robes, chains and hats. FREE, 10am-3pm

MAKING MASKS: The British Museum offers a free mask-making session to children aged 5+ and their families, inspired by objects in the museum's collection. Choose from ancient Egypt, the Aztecs, ancient Greece, Persia, Peru or Japan, and learn about the objects before using a tablet to create your own design. FREE, 10am-4pm

CRICK DISCOVERY DAY: Scientific institute The Crick invites the public inside for a family-friendly Discovery Day, including hands-on experiments, science shows, and a chance to interview a scientist. FREE, 11am-4pm

JAZZ AND FOOD FESTIVAL: Greenwich Peninsula holds a free-entry Jazz & Food Festival. In addition to live music and New Orleans-inspired food stalls, there's a vinyl market and a children's drumming workshop, among other activities throughout the day. A new mini golf course has just opened in the area too. 11am-7pm

WINE CAR BOOT: Coal Drops Yard in King's Cross hosts the Wine Car Boot, a market where each car boot or stall is an independent wine retailer, importer or producer with a selection of their current favourite wines for you to taste and buy. 12pm-8pm

LATIN MUSIC FESTIVAL: Taking place at Walpole Park in Ealing, Latino Life In The Park claims to be the UK's largest Latin American music festival, with five stages of live music throughout the day — including Colombian Independence Day celebrations on the main stage. 12pm-10pm

BACKGAMMON TOURNAMENT: The Andover Arms pub in Hammersmith hosts a backgammon tournament, with anyone welcome to enter (though you must do so by Friday to take part). There's a £5 entry fee, with prizes to be won. 2pm-8pm

LONDON'S QUEER HISTORY: Queer people have lived in London since its founding. Hear their stories on this Museum of London guided walk, which takes you through the City, spanning the periods through Roman occupation, the medieval period, and the English Civil War, telling stories of queer struggle alongside queer love and joy. Starts at the Royal Exchange and ends in Farringdon. 3pm

BUSH COMEDY FESTIVAL: Today's the final day of west London's Bush Comedy Festival, with seven different shows taking place throughout this afternoon and evening — beginning with Comedy Club 4 Kids. Later on, Emma Sidi, Paul Williams, Desiree Burch and Matt Forde are among the comedians offering solo WIP shows. 3pm-10pm

MUCH ADO ABOUT NOTHING: Dress for the weather and head to Brixton Windmill for an open-air production of Shakespeare's Much Ado About Nothing. Six actors in full Elizabethan costumes and a two-storey set take over Windmill Gardens for the show. 6pm

HAK BAKER: The Somerset House Summer Series comes to a close this weekend, and although tomorrow night's concert has sold out, there are still tickets available to see east London singer and rapper Hak Baker headlining the stage in the Somerset House courtyard tonight. Doors 7.30pm

COMEDY FESTIVAL FINALE: Another comedy bonanza coming to a close today is Balham Comedy Festival. The final show includes Joe Wells, Roger Monkhouse, Alexandra Haddow and Michael Odewale, with John Moloney as compere. Takes place at The Bedford in Balham. 8.30pm-11pm

SCARED TO DANCE: American musician John Grant is the guest DJ at tonight's Scared to Dance, an alternative club night playing post-punk, indiepop, new wave and art rock music. Takes place at the Shacklewell Arms in Dalston. 11pm

Sunday 21 July

HOT AIR BALLOONS: Cross your fingers that the weather's clement enough to allow dozens of hot air balloons to take to the skies in the early hours. The Lord Mayor's Hot Air Balloon Regatta was cancelled due to high winds two Sundays ago — if it goes ahead today, the flotilla takes off from Battersea Park in the early hours of the morning, and is a sight well worth seeing. FREE, from 5am

PETER AND THE WOLF: Introduce children to classical music and instruments at Opera Holland Park's family-friendly performances of Prokofiev's composition Peter and the Wolf. Storytelling, dance and spoken word also feature in the show, which lasts just 30 minutes and takes place in Opera Holland Park's auditorium. 10am/1pm

LORD OF THE RINGS: Not feeling Sunday? Miss it entirely by heading to the Prince Charles Cinema for a screening of the Lord of the Rings Trilogy: Extended Editions. It's all three films, shown back to back, in a marathon screening lasting more than 12 hours. 10.30am-11pm

DEEP DIVE: The newly-opened Museum of Homelessness in Finsbury Park now has an events programme up and running, including the monthly Deep Dive, a current affairs programme about homelessness hosted by the museum's directors Matt and Jess, along with special guests. Full details of this month's edition TBC at time of writing. FREE, 11am-12pm

SOHO VILLAGE FETE: A tug of war between the police and fire brigade, a best in show where pooches must dress like royalty, and a music stage are all part of the Soho Village Fete. But surely the highlight is the Soho Waiters' Race, which sees serving staff from different restaurants legging it around the area while balancing a bottle of fizz, wine glass and ashtray on their tray. FREE, 12pm-6pm

GARDEN TOUR: Take a guided tour around the gardens of Fulham Palace, learning how the space was used by successive Bishops of London. It's also a chance to see what the current garden team is working on, and view some of the unusual plant specimens kept there. Age 14+. 12.30pm-1.45pm

THE DANCE EXCHANGE: Southbank Centre hosts The Dance Exchange, a day of street dance workshops and performances, hosted by Chilly of Rain Crew UK. It's open to all ages, with intergenerational dancing very much encouraged. FREE, 1pm

JU DOU: Victor Fan from King's College London introduces Zhang Yimou's 1990 film Ju Dou, at the Garden Cinema in central London this afternoon. The erotic, fairy tale-like story of a woman married to a murderous dye mill owner, has been likened to the fantasy worlds of Powell and Pressburger. 1.30pm

THIRD WHEELIN': Folky vocals, lush piano and multi-instrumental talents are promised from jazz trio Third Wheelin', who are performing classic jazz standards, plus their own compositions, at ArtHouse Crouch End this evening. 6.15pm