What should one do in London?

[Louis VI the Fat]

the sensation that I could feel the rich history - old history. Not like Gettysburg or Valley Forge - much older. I remember walking along the Parliament building and seeing the statue of Richard the Lionheart

Sorry for bursting romantic views of the world, but this is one of my pet peeves.

Do you realize that Valley Forge is much older, and Gettysburg as old, as the Parliament Building and the Statue of Richard the Lionheart?

The United States is ancient, much older than most European states. In the nineteenth century, America was a forward-looking country, constantly renewing her legacy, whereas European states build and invented themselves traditions and a history during this period.

Americans travel to Europe, and go see, for example, Budapest and think they are in an ancient town. Never realising that except for maybe an old cathedral and a fortified castle everything they see around them was build in a historical style at the exact same time that Chicago was already building skyscrapers.

Splendid older monuments apart, most of London, like Paris, is nineteenth century, when the congested medieval town was replaced with wide streets and large appartment blocks. Alas, further twentienth century renewal hasn't been kind to London. I must agree with prince Charles that London has lost its historical character.

Which is not to say that London isn't the hippest, possibly most exciting city in Europe.

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As for what to do - that all depends on one's personal preferences. I usually just barge in and soak up the atmosphere. And..I am actually always proud of being a stupid tourist. I work off the list of famous landmarks that one ought to see. And then get some personal must-sees done. If I'd be in London right now I'd go see:
St. Paul's
Westminster
Canary Wharf
a Dickens tour
the Natural History Museum
Places from where I can avoid seeing that dreadful ferry wheel.

And I would:
Buy a retro-1980 Arsenal kit. One of those with devastatingly short trousers that are tighter and tinier than present day underwear. Then see a Tottenham match in it. Sit myself next to a few fat blokes, and shout for ninety minutes 'this what you (fl)ossers call football? Daylight robbery, I say, twenty quid for this (w)hite!?'

Stand an afternoon on Picadilly Circus. Blasting loud Norwegian Metal from my ghettoblaster, headbanging and shouting at the top of my lungs 'EnglishAssassin! Assassin! Where art thou?'