All week
BATSFORD PUBLISHING: A publisher of specialist non-fiction books, Batsford Publishing has been going for 175 years, having been established when Bradley Thomas Batsford opened a bookshop on High Holborn in 1843. A free exhibition about the publisher's history, featuring books (of course) and archive materials, closes this week. Holborn Library, free, just turn up,until 28 June
ROCK 'N' ROLL: It's the final week to see this exhibition of shots by music photographer Mark Allan. Over his 30 year career, he's worked with the likes of Bowie, Britney Spears, Tina Turner and Gorillaz, so there are big names to be seen in this show. Barbican Library, free, just turn up, until 29 June
FESTIVAL OF ARCHITECTURE: It's the final week of London Festival of Architecture, and there are plenty of free events. Visit interactive installations, look out for free outdoor art, and browse the programme for talks and tours that won't cost you a penny. Various locations and prices (some events free), until 30 June
CONNECTIONS FESTIVAL: National Theatre's Connections Festival is a youth theatre festival, where young people from across the UK come together to perform 10 newly-commissioned plays. Highlights include Flesh, about a group of teenagers who wake up in a forest with no idea how they got there, and Class, about the internal politics of a school election. National Theatre, £5, book ahead, 25-29 June
Monday 24 June
FREE BURGERS: Burger & Beyond in Shoreditch celebrates hitting 150k Instagram followers by giving away 150 burgers free. It's first come first served, eat in only (no takeaway), and applies to single cheeseburgers. Burger & Beyond (Shoreditch High Street), free, just turn up, from 5pm
STREET ART LAWS: Andrea Baldini — author of A Philosophy Guide to Street Art and the Law — talks about the relationship between urban graffiti and the law. It's a crucial relationship, as urban street artists depends on their ability to subvert the normal uses of public spaces. City, University of London (Clerkenwell), free, book ahead, 6pm-8pm
QUIZ: Put your trivia knowledge to good use at this team quiz night, which covers everything from films to kings and queens to London buildings. There's a chance to win a Canary Wharf gift card, and food and drink is available to order throughout the evening. Just be warned that the event is outside, so dress accordingly. Cabot Square (Canary Wharf), free, book ahead, 6pm-9pm
Tuesday 25 June
SALTERS' HALL: As part of London Festival of Architecture, Salters' Hall opens its doors for a free tour. Brutalist on the outside, the building is home to The Salters' Company, one of the City of London's livery companies. Inside, visit the ceremonial rooms and archives, which are rather more fancy than the exterior belies. Salters' Hall (Barbican), free, book ahead, 12pm-1.15pm/2pm-3.15pm
AIR POLLUTION: Another London Festival of Architecture event, is this panel discussion about the current state of London's air quality and how it can be improved. How can we tackle it, and who is ultimately responsible? Bush House (Strand), free, book ahead, 6pm-8pm
EDINBURGH PREVIEW: Comedian Rosie Jones offers a preview of her new show, exploring what it's like to be the world's first, and only, disabled, gay, northern comedian with a phobia of cotton wool and a lethal amount of Creme Eggs in her wardrobe. Pleasance Theatre (Islington), £5, book ahead, 7.45pm
Wednesday 26 June
MOVIE NIGHT: 2017 film Battle of the Sexes is shown for free on the big screen in Merchant Square. Starring Emma Stone and Steve Carell, it tells the true story of the 1973 tennis match between world number one Billie Jean King and ex-champ Bobby Riggs. Merchant Square (Paddington), free, just turn up, 5.30pm-7.30pm
PRIDE LATE: Science Museum flies the rainbow flag for a Pride themed late night opening. Listen to Europe’s longest running LGBTQ+ choir, the Pink Singers, or hear from Bishopsgate Institute archivists about the Stonewall riots. Plus there are talks, performances, a silent disco, and a chance to wander around the usual exhibits after dark. Age 18+. Science Museum (South Kensington), free, book ahead, 6.45pm-10pm
BRUSSELS: This month's Dash Cafe takes on Brussels/Brussel/Bruxelles, a city made up of different communities, languages, governments and neighbourhoods. Academic and activist Eric Corijn, poet Elisabeth Severino Fernandes, and writer and journalist Owen Hatherley all offer their take on the interconnected hub of a city, through short films and poetry. Rich Mix (Shoreditch), £5, book ahead, 7.30pm
Thursday 27 June
HYDE PARK NURSERY: This central London nursery — that's plants, not kids — is not normally open to the public, so this open day is a rare chance to get inside. See the advanced technology used in the building to grow plants for the Royal Parks' flower beds, take a free tour of the facility, and purchase a plant or two to take home (cash only). Hyde Park, free, book ahead for tours, 10am-5pm
BAZALGETTE'S BIRTHDAY: Engineering mastermind Sir Joseph Bazalgette — responsible for much of London's sewer system — would have been 200 this year. Attend a birthday party held in his honour, and find our more about his sewers, bridges, embankments and street designs. London Metropolitan Archives (Clerkenwell), free, book ahead, 2pm-3pm
BAKERLOO LINE EXTENSION: Members of the TfL Planning and Engineering teams provide an update on proposals to extend the Bakerloo line to Lewisham. Find out about the challenges and opportunities that are arising in the planning process, and hear about plans for the redevelopment and regeneration of the Old Kent Road. Institution of Civil Engineers (Westminster), free, book ahead, 6pm-8pm
Friday 28 June
GREAT EXHIBITION: The greatest exhibition that ever came to London is recreated. The Great Exhibition of 1851 was an epic showcase of cutting-edge technology, held in a purpose-built Crystal Palace in Hyde Park. The Great Exhibition Road Festival aims to recreate its spirit with free activities across more than 20 venues. South Kensington, free, some events require booking, 28-30 June
MUSEUM LATES: Natural History Museum stays open late for an evening looking at how technology such as 3D printing has changed what scientists can learn from specimens. Get close to the exhibits at pop-up science stations, visit the current Museum of the Moon, or attend a free talk about the Crystal Palace Dinosaurs. There are also LGBTQ+ tours of the museum, celebrating the diversity of nature. Natural History Museum (South Kensington), free, just turn up, 6pm-10pm
ART TALK: Londonist's Visual Arts Editor Tabish Khan chats to artist Richard Woods on the site of Woods's public art installation Holiday Home (White City). The work is part of the Kensington & Chelsea Art Weekend public art trail, and is one in a series of house-shaped identical sculptures called Holiday Homes. White City Place, free, book ahead, 7pm-7.30pm
Saturday 29 June
AGRICULTURAL SHOW: Mudchute Farm hosts its annual agricultural show, which includes livestock shows, baking competitions, rural craft demonstrations, a Shetland pony photo booth (we have questions about that one too...), local art and craft stalls, and plenty of food and drink — all in the shadow of the Canary Wharf towers. Mudchute Farm, free entry, just turn up, 29-30 June
TOWER BRIDGE: London icon Tower Bridge is 125 years old, and to celebrate, it's offering entry tickets for just £1.25 this weekend. It'd usually cost you £8.80-£9.90, so it's rather a bargain — the catch being there's no advance booking, so it's a case of turning up on the day and hoping it's not too busy. Tower Bridge, £1.25, just turn up, 29-30 June
SEVEN DIALS: Festival 30 marks the 30th anniversary of the Sundial Pillar in the middle of Seven Dials (the original can now be seen in Weybridge). Celebrations today include live music, theatre performances, arts and crafts activities. It's closed to traffic, with a pop-up lawn around the pillar, and KERB stalls are on hand to give a preview of the new market opening in September. Seven Dials, free, just turn up, 11am-6pm
Sunday 30 June
DRAGON BOATS: Dozens of traditional dragon boats go head to head at the London Hong Kong Dragon Boat Festival. Entries to race this year have closed, but you can still go along and watch, and enjoy entertainment including food stalls, live bands, a raffle and a carnival. Royal Docks, free to watch, just turn up, 8.30am-6pm
HANWORTH CLASSIC: Channel the 1940s and 1950s at the annual Hanworth Classic, a gathering of vintage cars, motorbikes, scooters and military vehicles. There's a festival vibe too, with live swing music, jive dancing and a barbecue. Bushy Park (Hampton Court), charity donation for entry, just turn up, 11am-4pm
SOHO VILLAGE FETE: Snail racing, a spaghetti eating competition and the legendary Soho waiter's race are all part of Soho village fete. See 40 waiters race around the streets balancing a bottle of champagne, a glass and an ashtray on their trays. St Anne's Gardens (Wardour Street), free, book ahead, 12pm-6pm (waiter's race 3.30pm)
