How can I come to London and not try to find the places that inspired JK Rowling to write the Harry Potter books? 
The place of the Leaky Cauldron has been changed over the course of the movies. One of its locations is a flower shop called Chez Michele in Borough Market. At first glance, you can't really tell that it's the same place but after a while you realize that with a makeover and the same paint job, the flower shop could be the Leaky Cauldron.
I have tried searching for the Diagon Alley look alike since I first got here but there never seems to be a definite place that inspired this wizarding street. I went to Cecil Court by Covent Garden but the street didn't remind me of the movies at all. It is full of bookshops and art stores but none of the building seems to resemble anything you'd see in Diagon Alley. I also went to Goodwin's Court. This street is quite narrow but the building and the windows definitely have a Harry Potter feel to them. I definitely have to check out Leaden Hall Market, where the Diagon Alley scenes were filmed!
And of course I have seen the places over which Harry Potter and his guard fly on their broomsticks. They fly over the river near Westminster, showcasing Big Ben and the Houses of Parliament. The opening scene in the 6th movie shows the Death Eaters destroying a bridge, the Millenium Bridge which is also in the same area.
The best monument London has to Harry Potter is Platform 9 and 3/4. It's located at King's Cross Station just like the books but is a little tricky to find. But once you do find it, you can take pictures as if you are on your way to the Hogwarts Express!