Update! I’ve done a bit of research into the clock, it is an astronomical clock installed by Bernard Bracken, Chairman of the Times newspaper, in 1955 as the newspaper was printed inside this building. The face in the middle is Winston Churchill. The little round window to the upper right of the face is of unknown function.
The building itself is made out of pink brick as this was the colour of the newspaper at the time.. I think the Financial Times is still pink??