The Slitheen take over Downing Street in episode 1x04 "Aliens of London". From episode 1x05 "World War Three". The Master kills his cabinet in the rebuilt Downing Street in episode 3x12 "The Sound of Drums".
Source: The Doctor Who Locations Guide
The Doctor drops Agatha Christie off at the hotel after an adventure in the TARDIS in episode 4x07 "The Unicorn and the Wasp".