Brigitte, I don't think there is one just covering the city, most do the whole of central London. The city isn't very big, it is sometimes referred to as "the square mile".
My suggestion, DIY bus tour with normal (red) buses, a lot cheaper. Buy an Oyster Card.
TFL (=Transport for London, them what runs the buses and tubes), publish a tourist map with selected central London bus routes: http://content.tfl.gov.uk/key-bus-routes-in-central-london.pdf
Or just use the TFL journey planner: https://tfl.gov.uk/plan-a-journey/
For anybody who doesn't know what "The City" is: It is the original medieval area of London, now the business and banking district. Contains St Pauls, London Bridge, The Tower, Bank of England, and a lot of tall buildings with banks and financial houses in them.
The other "centre" of London is Westminster, the government area with Houses of Parliament, government offices, royal palaces, Westminster Abbey etc.
These were originally two separate places, with fields in between, now merged into one humongous big city.