Just remember that if you're from any "normal" city, you will be blown away by what constitutes "inside London".
The population of London is >12 million, and it takes two hours to drive from one side to the other.
I lived in London for 4 years, in various boroughs (Westminster, Camden, Hammersmith) and it's a great town. In general, a 7 day travel card will serve you best - it lets you use the busses and tubes and some surface rail services.
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Overhead, the Albatross hangs motionless upon the air,
And deep beneath the rolling waves,
In labyrinths of Coral Caves,
The Echo of a distant time
Comes willowing across the sand;
And everthing is Green and Submarine
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