Here are some popular options:

1. Museums and Galleries: Many of London’s world-class museums and galleries offer free admission to their permanent collections. Some notable ones include the British Museum (https://www.britishmuseum.org/visit), the National Gallery (https://www.nationalgallery.org.uk), the Tate Modern (https://www.tate.org.uk/visit/tate-modern), the Science Museum (https://www.sciencemuseum.org.uk), and the Victoria and Albert Museum (https://www.vam.ac.uk/south-kensington).
2. Parks and Gardens: London is known for its beautiful parks and green spaces. Visit Hyde Park, Regent’s Park, Greenwich Park, and Hampstead Heath for a leisurely stroll or a picnic.
3. Changing of the Guard: Witness the ceremonial Changing of the Guard at Buckingham Palace. Check the schedule as it doesn’t happen every day.
4. Street Markets: Explore the various street markets, such as Borough Market, Camden Market, and Portobello Road Market. While you might be tempted to shop, browsing is free!
5. Southbank Centre: The Southbank Centre often hosts free events, including concerts, performances, and exhibitions along the Thames River.
6. National Theatre: The National Theatre on the South Bank has free exhibitions, backstage tours, and affordable ticket options for theater performances.
7. Trafalgar Square: Enjoy the vibrant atmosphere at Trafalgar Square and take a photo with the iconic Nelson’s Column.
8. British Library: Discover literary treasures at the British Library, including the Magna Carta and original manuscripts from famous authors. (https://www.bl.uk/visit)
9. Houses of Parliament and Big Ben: While you can’t enter the Houses of Parliament for free, you can admire the architecture and take photos from the outside. Big Ben (the tower’s actual name is Elizabeth Tower) is also a must-see.
10. Cultural Festivals: Keep an eye out for free cultural festivals and events happening around the city, such as Notting Hill Carnival or Diwali on Trafalgar Square.
11. More Libraries: Explore historic libraries like the Wiener Library and the Maughan Library at King’s College London, which are open to the public and offer fascinating collections.
12. Street Art: Wander through neighborhoods like Shoreditch and Camden to see impressive street art and graffiti.
13. Views from Primrose Hill: Hike up Primrose Hill in Regent’s Park for panoramic views of the London skyline.
14. Visit a Church: Visit iconic churches like St. Paul’s Cathedral and Westminster Abbey for their stunning architecture. Some may require a small donation for entry.

Remember that London’s public transportation system can be expensive, so consider walking or using a bike-sharing program to explore the city. Additionally, some attractions may have special exhibitions or areas that require an admission fee, so check their websites for details before visiting.