This capital is chock-full of incredible sites and experiences: you could easily while away weeks hopping between its abundant free museums, endless historic buildings, quirky markets and world-renowned restaurants. Although exploring London with kids in tow might seem overwhelming at first, it doesn’t have to be with this list of the best things to see and do. These places are buggy-friendly and easy to reach – and, most importantly, fun (yes, even for you). Here at Plum Guide, we've done all the hard work (as usual) and compiled this list of the best things to do in London with children for you to follow and enjoy.

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Let your little wizards see for themselves the magic and artistry that goes into making the Harry Potter films on the Warner Brothers Studio Tour. There’s the chance to wander the Great Hall and saunter down Diagon Alley before taking a broomstick ride – ending with a kid-friendly butterbeer, of course! Expect magic and photo opportunities at every turn, including wand-making demos, a chance to push a trolley through Platform 9 ¾ and board the Hogwarts Express. Children are given Harry Potter passports, so help them fill them up with stamps as the tour progresses.

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A trip to London wouldn’t be complete without taking your child to the world’s biggest and oldest toy store: Hamleys. Prepare to spend at least an hour or two (or four) at this Regent Street institution, and keep that cash or credit card ready. Within this wonderland of fun and frolics – complete with entertainers – there’s sure to be something the little ones will want you to buy. And don’t be surprised if you end up having just as good a time (no matter how much you want to deny it).

Equally bright and popular is the world’s largest LEGO store in Leicester Square, complete with a massive play area – perfect to occupy them on a rainy day. The world’s largest candy shop, M&M'S London, is just across from it. The kids can take home souvenir candies with their faces printed on them. Pretty cool if you have a sweet tooth.

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Attending a West End show is one of the best things to do in London with kids. You'll find an ever-changing yet no less impressive roster of kid-friendly shows, including Lion King, Matilda, Wicked, and Frozen. It’s best to book your tickets a few months in advance, but some theatres reserve tickets for shows on the day for the spontaneous (read: last-minute) among us. Just visit the ticket booth in Leicester Square to find out what’s available.

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Packed with hands-on, interactive displays about everything from outer space to aircraft and robots, the Science Museum in South Kensington is a winner when it comes to the best things to do in London with kids. While it’s free to enter and browse, one of the best places for children is the Wonderlab (entry fees apply here), with its magical Chemical Bar and eye-opening live science shows. If you don’t want to fork out for that special exhibit, the Pattern Pod, the Garden and the Basement will provide hours of free entertainment, and they’re excellent spaces for the kids to let off steam.

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Conveniently standing just next door to the Science Museum is the Natural History Museum. Of course, it’s got gigantic dinosaur fossils that children will love to gaze at, but it’s also home to 80 million other specimens – from the smallest insects to the biggest animals on Earth. Go on a hunt to find the clock from the CBeebies show Andy's Dinosaur Adventures. Both of these museums are located in Kensington and Chelsea, two of the best neighbourhoods in London for children. They're popular for families not only because of their proximity to some of the city’s greatest museums, but also because nearby is the magical Peter Pan-themed Diana Memorial Playground in Kensington Gardens. Can’t make it to the museum? Take a virtual tour instead.

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Enter a mini city built just for kids at KidZania London. Just like they would in the real world, the kids can earn and spend money (Kidzos, not actual pounds) and try out a range of different careers, from being a TV presenter or chocolatier to working in a hotel or supermarket. It promotes independence as they’re encouraged to take part in the activities without you watching over them. While they’re busy, do a bit of retail therapy in Westfield shopping mall. You deserve it.

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You can't visit London with little ones in tow without stopping by ZSL London Zoo. Set in Regent's Park, this sprawling zoo hosts animals from around the world. Alongside learning about their habitats and habits, you'll be able to teach the kids about endangered species and wildlife conservation. If your 11 to 15-year-old fancies themselves a zoologist, you can even arrange 'Junior Keeper' experiences where they can meet the animals up close – how special is that?

If London Zoo seems a bit too much, try Battersea Park Children's Zoo instead. It's home to lots of small animals and birds, so don’t go expecting the big five here. Still, it's ideal for families because it’s a much less crowded alternative – and there’s no way near as much walking involved – so little explorers won’t tire too quickly (and neither will you, for that matter). As well as petting and feeding the farm animals, wannabe farmers can try out a real-life tractor for size, and there’s a big adventure playground.

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One of the best things to do in London with kids is quite simple... eat. You'll find plenty of child-friendly restaurants throughout the city, whether they're in the mood for pizza and burgers or something more upscale. Kids 8 years old and under eat free at selected Gordon Ramsay restaurants – who can say no to a free meal?

For something more informal, London’s market-style eating spots are easy pleasers: Market Hall Victoria, Spitalfields, Borough Market, Box Park and Mercato Metropolitano have something for everyone. Take breakfast to a new level at Cereal Killer Café, which sounds super gimmicky, but the kids love it because it stocks every cereal under the sun. Let them mix and match to create their own colourful creations. Mexican restaurant Wahaca gives colouring sheets and pencils to keep kids busy, while Pan-Asian restaurant Inamo has tables that double up as entertainment centres where you can play games and order food with a tap. Hit two birds with one stone at American diner All Star Lanes, which has its own bowling alleys.

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• Our Guide to Where to Stay in London with Kids

• The most unique things to do in London

• 9 of the best places to eat in London

• The Perfect London 3 Day Itinerary