A colloquialism for 10 Downing Street, the official residence of the British Prime Minister in office. Bracing Number 10 is, of course, Number 11, the residence where the Chancellor of the Exchequer resides. The address has also been brought into the internet as the PM's official web site at www.number-10.gov.uk.
Number 10 began its life as a mansion leased to Justice of the Peace Sir Thomas Knyvet, and later was passed on to the aunt of Oliver Cromwell. The facade of the house is the result of one George Downing, whom the street is named after, after acquiring the rights in the 17th century under somewhat shady circumstances.
The house became an official government residence in 1732, and the first government officer to habitate it was Sir Robert Walpole, the first Lord of the Treasury (and, informally at the time, the first Prime Minister), in 1735. Sir Walpole set the property as residence for all future First Lords of the Treasury, and office that evolved into the office of the PM.
Number 10 has evolved over the years to fit the times. A grand Dining Room was build in 1820, and the surrounding buildings were pulled down in 1860 to be replaced by administrative offices. The house was electrified and telephied in 1894. Structural stabilizing work was done throughout the 1960's, and ethernet was installed in the mid-90's, so there is a chance that the Honorable Tony Blair (the current PM) could be reading this very writeup from inside the very house I'm speaking of.
As an interesting sidenode, the PM (who lives there), does not have keys to the house, but instead there is always a duty officer waiting to open the main door.
Citations: www.number-10.gov.uk