Here's an ideal itinerary for 2 days in London:

Day 1:

• Start your day with a visit to the iconic Tower Bridge. You can walk across the bridge and take in the stunning views of the River Thames.
• Next, head over to the Tower of London, which is just a short walk away. This historic castle has been home to many famous prisoners and is also where the Crown Jewels are kept.
• After exploring the Tower of London, take a stroll along the South Bank of the Thames. You'll find plenty of street performers, food vendors, and shops to keep you entertained.
• For lunch, head to Borough Market, one of London's oldest and most famous food markets. You'll find everything from fresh produce to artisanal cheeses and baked goods.
• In the afternoon, visit the British Museum. This world-renowned museum houses some of the most important artifacts from around the globe, including the Rosetta Stone and the Elgin Marbles.
• End your day with a visit to Covent Garden, a bustling area filled with shops, restaurants, and street performers.

Day 2:

• Start your day with a visit to St. Paul's Cathedral. This iconic cathedral is one of London's most recognizable landmarks and offers stunning views of the city from its dome.
• Next, head over to the nearby Tate Modern, one of the world's most famous modern art museums. The museum is housed in a former power station and features works by artists such as Picasso, Warhol, and Hockney.
• For lunch, head to Brick Lane, a vibrant area known for its street art and diverse food scene. You'll find everything from Indian curries to bagels and falafel.
• In the afternoon, visit the Houses of Parliament and Big Ben. You can take a guided tour of the historic buildings and learn about the history of British politics.
• End your day with a visit to the West End, London's famous theater district. Catch a show at one of the many theaters in the area or simply stroll around and take in the lively atmosphere.

I hope this itinerary helps you make the most of your time in London!