Henry Campbell-Bannerman

The framed photograph of a man who had served as Prime Minister of the United Kingdom was present on the stairs of 10 Downing Street, alongside photographs of other previous holders of the office, in 2006. (TV: '')

Behind the scenes
While unspecified in the episode, the photograph is of Sir Henry Campbell-Bannerman, a Liberal Party politician who served as Prime Minister from 1905 to 1908 in the real world.