If you intend to visit the centre of London on a tourist bus, I will recommend another option that can be free if you have an Oyster Card or a Travelcard.
Bus 159
This is the regular bus line 159, the classic red double-decker bus just like the tourist bus. It has the disadvantage of the absence of the tour guide, but nothing that our Essential London tour cannot solve. You can stop at the places that interest you most and return to the route where you left off as the frequency of passage is 4 to 8 minutes on weekdays and 10 minutes on weekends. This bus is operational 24 hours a day.
If you have a Travelcard, you can get on and off the bus as many times as you need. If you are using an Oyster card pay-as-you-go, you will pay for each trip you make. Remember that on London buses you cannot pay in cash.
Sightseeing tour
The 159 bus will allow us to see all the Westminster icons. I recommend you start at Oxford Street. It is one of the most commercial streets in the world and ideal for shopping. You will arrive at Oxford Circus and the bus will turn right to continue on Regent Street also known for its shops. Then you will arrive at Piccadilly Circus Square where you will see the memorial fountain to Lord Shaftesbury and Eros.
The bus continues through Haymarket to Trafalgar Square where you can see the Admiral Nelson Memorial Column and the National Gallery Museum. You can also see the Admiralty Arch which gives access to The Mall which you will recognise by the reddish colour of the asphalt and which leads to Buckingham Palace.
You will pass through Whitehall and if you look to the right you will see the Ministry of Defence and the Horse Guards where you can see the mounted guard and the tourists taking pictures. You will then pass Downing Street famous for housing the British Prime Minister's residence in building number 10. You will also see the Treasury building and in front of the Cenotaph, a monument to the fallen of the First World War.
You will then reach Parliament Square and see Westminster Abbey as well as Parliament, which gives the square its name. The bus will take you to the River Thames under the Big Ben, past the Westminster Bridge and if you look to the left you see the London Eye, an impressive white Ferris wheel, and to the right the London Aquarium, recognisable by its curved façade.
I would advise you to finish the route at this point as there is nothing interesting to see the rest of the way.
Other lines and routes
If you want to know other areas of London, besides the bus 159, you have other interesting public service lines to do sightseeing in London.
Lines 9 and 15 are heritage routes because they are partly run by the traditional red two-storey Routemaster buses, which are accessed from the open back. These buses are being replaced by more modern ones, but some Routemaster are preserved for their heritage and tourist value.
Bus 15 runs from Trafalgar Square to Tower of London, through parts of Westend, City and East London and you can see Saint Mary Le Strand, Saint Clement Danes, Temple Church, St Paul's Cathedral and Monument.
Bus 9 runs from Trafalgar Square to Warwick Gardens and passes Picadilly Circus, Hyde Park, Green Park and Kesington Gardens.
Bus 11 runs from Fulham Broadway to Liverpool Street, passing Sloane Square and its shops, 10 Downing Street and White Hally, Trafalgar Square, Fleet Street, the Bank of England and the City. See monuments such as the Roman Temple of Mitra, St Paul's Cathedral, and Westminster Abbey. The tour lasts just over an hour. And although most of the service is done with modern buses, still retain some Routmaster.