If you are in london ever do these things; you will love it. Spend weekends at the banks of Thames drinking beer and going through the several street vendors selling second hand books. The historic town will carry you away into the past and you
will become part of what happened there centuries ago.
Watch a Shakespeare play in the globe theatre and when you think that Shakespeare himself conducted plays there, the experience builds up multiple folds.If you don’t get a place to sit and even if it rains stand in the open theatre and watch as King Lear majestically deliver his lines. It is priceless
Spend a whole day at the National Gallery even if you are ignorant about paintings, Go and Chose one large painting and sit in front of it and look at it for an hour. You will either be transported into it, or the characters from the painting will walk out and interact with you.
Live a few days from a station locker room. Rent a locker for 5 pounds and keep your luggage there and travel london. Late night come back pick your luggage, use the restrooms to freshen up and then loiter around and sleep in the station. Morning again get freshened from the restroom take a locker for another 24 hours, Keep the bag there and see London again
You will enjoy London, This was how I experienced it and loved it