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The traditional old-style red double-decker bus (with a conductor and an open platform at the back) was a much-loved part of London's furniture, so when they were phased out in 2005 for the new-style bendy buses, lots of people were aghast. Luckily, the Mayor decided to keep a few of the old 1960s buses running on two "heritage routes".
So how about forgoing the tube for a day, and taking a trip on part of London's history?
The first route is No.9, and runs between Trafalgar Square and Kensington High Street:
Trafalgar Square --> Piccadilly Circus --> Piccadilly --> Hyde Park Corner --> Knightsbridge --> Royal Albert Hall --> Kensington High Street
The second route is No.15, and operates between Trafalgar Square and the Tower of London:
Trafalgar Square --> Strand --> Aldwych --> Fleet Street --> Ludgate Hill --> St. Paul's Cathedral --> Mansion House --> Cannon Street --> Eastcheap --> Tower of London
[Note: The heritage routes operate between 9.30 AM and 7 PM. Modern buses also operate on the same route, with extended hours/routes -- so make sure you board the right one. The heritage buses have an open platform and staircase at the back.]