Number 10 Downing Street has been the official residence of the Prime Minister since 1732. There is no general public access to it.
The Chancellor of the Exchequer traditionally lives next door, in number eleven.
However, when Labour came to power in 1997, the Prime Minister, Tony Blair, and the Chancellor, Gordon Brown (who became Prime Minister in 2007) swapped residences to enable the Blair family to have more room. This had never happened before.
See Number 10 Downing Street on the royal walk.