What is “Whitehall” in British politics?
As others have pointed out it is a geographical location in the heart of London within easy walking distance of the Houses of Parliament, Buckingham Palace, and 10 Downing St where the Prime Minister lives. Also its quite handy for all the well established Gentlemen’s Clubs where the wealthy disport themselves. Because of its convenience many government departments were at one point head-quartered there. Saying that something is being decided at Whitehall then is a shorthand way of saying that the Civil Service leadership in London is dealing with a matter. Possibly it is a bit like an American saying that Washington is dealing with a matter of vital concern to Oklahoma. It has a negative connotation in two senses firstly because the decision is being made by the state and nobody else and secondly because it is being taken in a place and by people who are remote from the realities about which they are deciding.
