What to see in London having only three days!
Where to begin if not from the central area and the symbol of London? The Palace of Westminster and the Big Ben Tower (underground station “Westminster”). After that, going through the bridge, you can easily get to the London Eye.
If you like walking, following the stream of the Thames, you will arrive to the Globe, that is the reconstruction of the famous Shakespeare Theatre, and to Tate Modern that is a Modern Art Museum. The entrance at the Tate Modern is free like all museum in London, so I recommend to go to make even a fast lap in the main ones because it’s worth it! From here you can see, and reach, the Tower Bridge and visit the museum of the London Tower.
Directing your gaze to the sky you will notice a very high building: it is the Shard, si tratta dello Shard, the highest skyscraper in the European Union designed by Renzo Piano and opened in 2012. Go up to the 72nd floor is not exactly cheap, but the view is breathtaking! To see alike this panorama, without spending a ridiculous amount, I recommend you to book a breakfast or an afternoon tea in Aquashard restaurant that is located on the 32nd floor of this skyscraper! [website for booking: ] /
A visit in the famous store Harrods is a must!(underground station Knightsbridge)
If you like visiting churches and cathedrals, or you like the architecture of religious buildings, i recommend you a visit to the Saint Paul Cathedral (it’s worth seeing it even only from outside).
For lovers of Harry Potter saga instead a fundamental step is the King’s Cross train station where you can take a picture at Platform 9 3/4 with the scarf of Gryffindor, Slytherin, Hufflepuff or Ravenclaw!
For those who are very passionate about this saga, there are the Warner Bros Studios where movies were filmed! Be warned though that the Studios are a bit out of London and the ticket price is £ 30. 
Then I recommend you to visit the Camden Town Market and in particular the “Cyberdog” shop in which you will find soft lighting, disco music and a lot of fluorescent clothes and accessories!
If you will be there for lunch time, try the typical dish Fish & Chips at Poppies , a 50s style restaurant. [address: 30 Hawley Crescent, Camden Town]
Finally I would suggest a visit to the British Museum and / or shopping in Oxford Street.
In the morning you can go and see the changing of the guard at Buckingham Palace and take a walk in St James park, full of squirrels!
If you will be in London on Saturday you must visit the characteristic antiques market of Portobello in Notting Hill neighborhood.
Then you could go and see the famous wax museum Madame Tussauds, or, if India fascinates you, go visit a little-known Indian temple: Shri Swaminarayan Mandir.
Finally I would suggest a visit to the National Gallery.