In London:

• The London Eye
• National Portrait Gallery
• Buckingham Palace (just outside tho, couldn't be bothered with the line)
• Houses of Parliament tour/Big Ben
• The Tate Modern
• Harrods
• Victoria and Albert Museum
• Madame Tussaud's Wax Museum
• Tower of London
• London Dungeon
• Shakespeare's Globe
• Camden Market (fav. place to go shopping!!!)
• Royal Observatory Grennwich
• National Maritime Museum
• Old Royal Naval College
• Kew Gardens
• Speaker's Corner
• several musicals and plays :D
• Kensington Palace
• St. Paul's Cathedral

Outside of London:

• Arundel Castle
• Hampton Court Palace
• Oxford
• Bath
• Stonehenge
• Windsor Castle