I always begin my London walking tours at Trafalgar Square. From Trafalgar you have easy access to the tube and you can begin walk #1 by foot. While standing in the center of Trafalgar square you have Nelson's column as a great starting point. Everyone loves to get their picture taken on the lions at the bottom of the column. If you face north you will see the National Gallery, which is free like most Museums in London. To your left is the Canadian embassy and to the right you will see St- Martin in the fields Church (church of the homeless). Now let's turn to the soutwest and begin the walk.
If you travel about 200 meters you will find yourself underneath Admiralty Arch and at the beginning of The Mall (red road leading to Buckingham Palace). Turn left on Horse Guards road and you will have St James park on your right and the Admiralty building on your left. Follow Horse Guards road to the Queens Horse Guards parade grounds on the left, head towards the stables which will bring you through an arch to Whitehall. Beneath the arch you will see the guards and the horses. Make a right on Whitehall and head towards 10 Downing street which will be on your right about 400 meters down the road. From the Prime Ministers residence make your way down towards Parliament and Big Ben but don't forget to look for the Red Lion pub (made famous by Winston Churchill). After you pass the Parliament buildings cross the street and head towards Westminster Abbey before making your way back to St James Park. Once in the park head east towards Buckingham Palace.
If you start the walk around 10am you should reach Buckingham palace in time for the changing of the guard. If you will be stopping along the way don't forget to give yourself more time. Check out the map below for walk #1(click to enlarge). Other London walking tours will follow.