Here's a fun-filled itinerary for 5 days in London that is perfect for families:

Day 1: Arrival and Exploring the City

• Start your day with a hearty breakfast at one of the many cafes in Covent Garden.
• Take a stroll through Trafalgar Square and admire the iconic Nelson's Column.
• Visit the British Museum, which has an impressive collection of artifacts from around the world.
• In the evening, head to Leicester Square to catch a family-friendly show at one of the West End theaters.

Day 2: Discovering London's History

• Begin your day by visiting the Tower of London, where you can see the Crown Jewels and learn about the history of the Tower.
• Take a walk across Tower Bridge and enjoy the stunning views of the River Thames.
• Head to St. Paul's Cathedral, one of London's most famous landmarks, and climb to the top for panoramic views of the city.
• End your day with a visit to the Globe Theatre, where you can watch a Shakespearean play.

Day 3: Exploring London's Parks

• Start your day with a picnic in Hyde Park, one of London's largest parks.
• Visit the Natural History Museum, which has interactive exhibits that are perfect for kids.
• Take a stroll through Kensington Gardens and visit the Diana Memorial Playground, which is inspired by Peter Pan.
• End your day with a visit to the London Eye, where you can enjoy breathtaking views of the city from above.

Day 4: Visiting London's Markets

• Begin your day by exploring the vibrant Camden Market, which has a variety of food stalls, vintage shops, and street performers.
• Visit the nearby ZSL London Zoo, which is home to over 750 species of animals.
• Head to Borough Market, where you can sample delicious food from around the world.
• End your day with a visit to the Southbank Centre, which has a variety of family-friendly events and activities.

Day 5: Exploring London's Museums

• Start your day with a visit to the Science Museum, which has interactive exhibits that are perfect for kids.
• Visit the nearby Victoria and Albert Museum, which has a collection of art and design from around the world.
• Take a stroll through the nearby Harrods department store, which is famous for its luxurious goods.
• End your day with a visit to the Westfield Shopping Centre, where you can shop for souvenirs and enjoy a meal at one of the many restaurants.

I hope this itinerary helps you plan your trip to London!