All weekend

FASHION CITY: This is the final weekend of Museum of London Docklands' Fashion City exhibition, showcasing the contributions of Jewish designers towards making London a fashion powerhouse. Items on display include a famous red coat worn by Princess Diana, and costumes belonging to Dot Cotton from EastEnders. Until 7 July

HAMPTON COURT GARDENS: The gardens at Hampton Court Palace have regular open days throughout the year, when the public can visit without paying the usual admission charges. This time round, they last all week, giving you seven days to explore the Privy Garden, Kitchen Garden, Pond Garden and other areas. Note that there's still a charge to visit the palace itself, the Maze, and the Magic Garden Playground. Free, 1-7 July

SUMMER SCIENCE EXHIBITION: The Royal Society's annual Summer Science Exhibition is a free interactive experience for anyone curious about the latest advances in science and technology. Take part in drop-in workshops, meet scientists and researchers, and find out about topics such as child language acquisition, processed foods, AI and creativity, and the future of medicine. FREE, 2-7 July

GARDEN FESTIVAL: Didn't make it to the Chelsea Flower Show? Head to the RHS Hampton Court Palace Garden Festival instead. Wander the palace grounds to see specially-designed gardens, and enjoy demos on gardening and floristry, from experts including horticulturalist Martin Fish, actor and passionate gardener Caroline Quentin, and 'Drag Queen Gardener' Tom Leonard. 2-7 July

WIMBLEDON: This is the first weekend of this year's Wimbledon tennis tournament. Heading down there to watch? Get clued up on how and when to queue for Wimbledon tickets — and be warned that Wimbledon Station isn't actually the closest stop to get there. Can't make it in person? Plenty of places around London show the action live on big screens — many of them free.  You can even tuck into a tennis-themed afternoon tea while you watch at the Ham Yard Hotel. Until 14 July

REJECTS EXHIBITION: With the Royal Academy's legendary Summer Exhibition now underway, see the artworks which didn't make the cut. REJECTS exhibition at Stokey Pop Up on Stoke Newington High Street showcases work by some of the 14,000 applicants who weren't chosen by the judges this year, including a painting of a woman punching Cupid, and a prize-winning loaf of bread. FREE, 4-14 July

IDLER FESTIVAL: Comedians, writers, musicians and philosophers take to the stage at Idler Festival, happening at Fenton House in Hampstead. Across three days hear from former Archbishop of Canterbury Rowan Williams on the Seven Deadly Sins, zoologist and author Lucy Cooke about why sloths are misunderstood, and novelist Zadie Smith about her life and work, among many others. 5-7 July

RIVER STAGE: Every weekend in July, the River Stage pops up outside the National Theatre on South Bank, offering free performances spanning music, theatre, dance, family workshops and club nights. The team behind LGBTQ+ bar The Divine curate this first weekend, hosted by Jonny Woo and John Sizzle. FREE, 5-28 July

EEL PIE ISLAND: The second of this summer's open weekends at Eel Pie Island offers a chance to set foot on the mysterious and private island in the Thames and visit the artists who live and work there in their studios — and of course, buy artworks straight from the source. FREE, 6-7 July

TURNER AND THE ENVIRONMENT: There's a new exhibition at Turner's House in Twickenham, the former home of artist J.M.W Turner. A World of Care: Turner and the Environment looks at how his work portrayed environmental and social developments — including burning furnaces and deforested landscapes — that would go on to change Britain and the world's climates forever. From 6 July

UNDERBELLY FESTIVAL: Pop-up culture venue Underbelly Festival is back in Cavendish Square, offering a slice of Edinburgh Fringe for anyone who can't make it to Scotland. Cabaret, circus and comedy shows are on the programme, as well as family entertainment, and there are bars and street food traders to keep you fed and watered. This weekend, catch adults-only parody show Dizney In Drag, or family-friendly comedy Mr Sleepybum. Until 21 September

BARBIE: One of the most anticipated exhibitions of the year opens at the Design Museum, focusing on one of the world's best-loved toys. Museum curators worked in partnership with Mattel Inc, and were given special access to the Barbie archives in California to put together Barbie: The Exhibition. 180 dolls feature, including a rare first edition Barbie from 1959, and the first Black, Hispanic and Asian dolls to bear the Barbie name, as well as the first Barbie with Down syndrome, and the first to use a wheelchair. 5 July-21 February

Saturday 6 July

URBAN BIRD WALK: Leica Ambassador, nature guide, wildlife photographer and cameraman Luke Massey leads an urban nature walk through central London, beginning at the Leica shop in Mayfair. The latest Leica binoculars are available to borrow for the walk, helping you to get a closer look at some of the area's wildlife. 10.30am-1.30pm

FAMILY STORYTELLING FESTIVAL: London Dreamtime brings storytellers from around the world to Southwark Park for a free family storytelling festival. Six storytellers take to the stage throughout the day, with BSL interpretation provided for the afternoon sessions. FREE, 11am-4.30pm

FESTIVAL OF STUFF: The Institute of Making hosts a Festival of Stuff, celebrating the joy of making and materials, at its Stratford HQ. Try throwing clay on a pottery wheel, experiment with casting metal, or learn the tricks of the blacksmithing trade, among other workshops and activities, with live music thrown in too. FREE, 1pm-5pm

SEWING MACHINE MUSEUM: The monthly opening of London's Sewing Machine Museum — located in Balham — takes place today, offering you a chance to see inside one man's collection of the machines. Many of them are historic, including one which belonged to Queen Victoria's daughter. Here's some more background on the little-known museum. 2pm-5pm

EUROS: Two Euro 2024 quarter finals take place today, and at time of writing, we now know that — thanks in no small part to Jude Bellingham — England will play Switzerland at 5pm. These venues around London will be screening the action, or check out London's best pubs and bars for watching football. 5pm/8pm

COSMIC DISCOVERY: Professor of Physics David Jamieson is at the Royal Institution to talk about the discoveries made by Galileo in the early 17th century. He used a new telescope to unearth Jupiter's moons, Venus's phases, and lunar landscapes, as well as discovering a 'fixed star' — which we now know as Neptune. 7pm-8.30pm

LION KING CONCERT: Hakuna Matata! The 30th anniversary of Disney animated film The Lion King is celebrated with a special screening at the Royal Albert Hall, accompanied by the Chineke! Orchestra and London Community Gospel Choir, performing Hans Zimmer's Oscar-winning score live. 7.30pm

SUMMER PARTY: Regular disco night Club de Fromage throws a summer party at its regular venue, the O2 Academy in Islington. Dance the night away to tunes by the likes of Lizzo, Queen, Beyonce, Taylor Swift, The Killers, ABBA and Avril Lavigne. Summer outfits are very much encouraged, and there's queue jump for anyone in fancy dress. 10.30pm-3.30am

Sunday 7 July

HOT AIR BALLOONS: Today is the first of three Sundays in July put aside for the Lord Mayor's Hot Air Balloon Regatta. If weather conditions are rights, dozens of balloons in various designs (and shapes) will float across the capital from Battersea Park first thing in the morning — from about 5am in fact, so set your alarm. Keep an eye on the website a couple of days before the event for confirmation as to whether it's happening today or not. FREE, from 5am

JOE WICKS FESTIVAL: 'The Body Coach' Joe Wicks — who became known for leading online workouts during lockdown — hosts a new wellness event at Kew Gardens. Joe Wicks Festival is a family-friendly day of activities including talks, yoga sessions, sound baths, talks, a picnic and more. 9.30am-6pm

DRAG QUEEN STORY HOUR: Aida H Dee — The Storytime Drag Queen — takes on the role of a drag queen that just cannot remember where she placed her spare wig, for Drag Queen Story Hour at the Regent's Park Open Air Theatre. It's aimed at children aged 3+ and their families. 10am/1pm

YACHT CLUB OPEN DAY: Twickenham Yacht Club invites members of the public inside for an open day. Have a go at sailing or paddle boarding on the river, and find out more about the club and becoming a member. FREE, 11am-3pm

CRAFT & FLEA MARKET: Makers, collectors, designers and creatives come together under one roof for the Walthamstow Craft & Flea Market, taking place at Big Penny Social. Vintage bric-a-brac, plants, jewellery, food, ceramics and candles are among the items available to buy from local and independent businesses and craftspeople. 11am-5pm

CHESS FEST: Trafalgar Square hosts a free chess festival, open to all, whether you're a seasoned player or want to learn the game. This year's Chess Fest has a theme of Alice Through the Looking Glass, and once again includes a living chess set with 32 actors taking on the role of the pieces. FREE, 11am-6pm

HAMPSTEAD BIG FAIR: Heath Street in Hampstead goes traffic-free for the Hampstead Big Fair, with 100 stalls selling crafts, food and drink, alongside a funfair, circus school, live music and other entertainment. FREE, 12pm-5pm

THE CALLY FESTIVAL: Islington's Caledonian Road — affectionately known as 'The Cally' — closes to traffic and puts on its party gear for The Cally Festival. The free-entry celebration of local culture has previously included live music, storytelling, workshops, kids' activities and more — full 2024 details TBC at time of writing. FREE ENTRY, 12pm-6pm