One of the pastimes that I have trained the most, here at London, is walking far and wide, and since I live near the Thames it has always been natural for me to dedicate sunny days to the river and its banks.
When I met Via che si va a Londra he told me that he had already frequented London and had already visited the surroundings of London Eye and Houses of Parliament, as all good tourists must have done on a trip to London, yet I can't help but advise her to have a good afternoon on one of my favorite walks.
The starting point is quite relative, it really depends on what your travel plans are, but generally I always prefer to start from Westminster Bridge and continue towards London Bridge, this way I often meet most of the tourists at the beginning of the walk and can enjoy some quiet for the rest of the journey.
Relative tranquility of course, remember that you are still in one of the most touristic cities in the world!
If you really want to do things right, you could start from Lambeth Bridge, and see the parliament for once also from a different perspective, compared to the classic tourist photos that are almost always taken from the London Eye.
Continue through i Golden Jubilee Bridges and the Southbank Center, after which you will meet Waterloo Bridge and the National Theater, up to Blackfriars Bridge, where you can decide whether to stop for a visit to the Tate Modern or continue your walk until Millennium Bridge, where you can enjoy a beautiful view of St. Paul's Cathedral.
Continuing you will come to London Bridge and this can be a great time to visit Borough Market or take a break from Monmouth Coffee, or continue to the world famous Tower Bridge and take a look at the Tower of London.
The tour is feasible in one afternoon, give yourself a day instead if you decide to stop several times along the way: you will have so seen half the wonders London and it won't cost you a pound.