You could pay for a guided tour of London or, for the cost of a Travelcard or an Oyster Card, you could organise your own excursion. With the help of a good guide book and the right bus you can see all the famous sights in your own time, lingering where you fancy without running to someone else's schedule.
Buses are a great way to get around London. I use them often. Slower than the tube but you see so much more and get a feel for the layout and size of the city which is impossible when you are underground.
If you are in London for a day then choose a Travel Card. Remember that most of the famous sights are in Zone 1 so don't buy a ticket for all the zones, 1-6 as it costs more. The fare you pay is related to the number of zones you travel through. If you are staying longer than a day then it's worth buying an Oyster Card. There's a 5.00 deposit refundable at the end of your visit. If you live in the UK you can buy your card online. Both cards allow unlimited travel on buses and underground trains.
Here are three of my favourite bus routes from which to see the sights.
NUMBER 11 BUS: Chelsea, Victoria, Westminster, Trafalgar Square, Aldwych, Fleet Street, St Paul's, Bank of England.
NUMBER 22 BUS: Chelsea, Sloane Square, Knightsbridge, Hyde Park Corner, Green Park, Piccadilly Circus.
NUMBER 9 BUS: Piccadilly Circus, Trafalgar Square, Strand, Aldwych [Covent Garden].
Enjoy your time everybody!