A lot of people take pictures of Big Ben as a starting london point, but the thing is, if you want to take a nice picture, climb one of these, usually the urbanest hotel is the prime spot for photographers to take a straight shot into the clock tower face.
London Canals are never on any touristy map, but deserve a good stroll, choose Regent's Canal and walk it to Camden, or the other way to Little Venice and submerge yourself into a London path where tourists you will find are close to none.
This is a famous skyscraper, but something not yet that famous is that on top floor you have a garden, called Skygarden, which apart from yoga events and other fun stuff has an amazing view, quiete identical to the shard for free. Even though sometimes you better book online most of the time just need to appear in front and ask if you can come in 9/10 they will let you in.