(by extension,idiomatic) The title or office of the Prime Minister.
2001,Trevor Owen Lloyd,Empire: the history of the British Empire, ISBN 1852855517, page 138:
... he declared from early in his life that he intended to be viceroy of India, as a natural stepping-stone on his way to 10 Downing Street.
(by extension,idiomatic) The government of the United Kingdom.
2006,Great Britain: Parliament: House of Commons: Public Administration Select Committee,Propriety and Honours: Interim Findings; Fourth Report of Session 2005-06, volume 29, ISBN 0215029798, page 23:
... explicitly clear, in the way that 10 Downing Street has made it clear in the case of city academies, that it is perfectly legitimate to put people in the House of Lords ...