Who resides at No. 10 Downing Street?

The English Prime minister resides at No10 Downing Street (currently Gordon Brown Feb 2008)

and his name is Gordon brown.

One small problem with the above Gordon Brown is the British Prime Minister & He's SCOTTISH ! Please refer to 'England ' as either GB or UK. England is part of the British Isles and part of the United Kingdom & although I am English, living in England, my Scots, Welsh & Irish compatriots do not enjoy being ignored...............
The UK PM ... United Kingdom's or alternately Britain's Prime Minister lives there. It's referred to quite commonly there and in the US as "Number Ten Downing Street"

... the US equivalent would be "1600 Pennsylvania Avenue", for The White House.
The incumbent Prime Minister.