The county is Buckinghamshire.
Buckinghamshire
The official residence of the Prime Minister of the United Kingdom is;10 Downing StreetLondonSW1A 2AAThe Prime Minister has a country house where he can spend some of his time, called Chequers, near Aylesbury in Buckinghamshire.
As with all British Prime Ministers for the past 200 years or so, his official London residence was no.10 Downing Street, but he also had the use of the country estate of Chequers, which was gifted by the nation for the Prime Minister's use in 1917. However, he also had his own private house in his constituency of Sedgefield, in the North East of England.
There isn't one really- the official London residence of the PM is Number 10 Downing Street, with the Chancellor living at no.11, but people often just refer to the Prime Ministerial residence as 'Downing Street', omitting the house number. The PM also has a country residence called Chequers, near Aylesbury in the county of Buckinghamshire, but this is the estate's proper name and not a nickname.
The Prime Minister lives at Number 10 Downing Street. There is a country residence for the PM at Chequers in Buckinghamshire.
D. H. Elletson has written: 'Maryannery' -- subject(s): Marriage 'Chequers and the Prime Ministers' -- subject(s): Chequers (England), Country homes, Dwellings, History, Prime ministers 'Roosevelt and Wilson' -- subject(s): Politics and government, Roosevelt, Theodore, 1858-1919, Wilson, Woodrow, 1856-1924
The Prime Minister of Britain lives in 10 Downing Street, London, England, whilst in office.
Generally presidents have an 'official' residence. What and where that residence is would depend on which country you are referring to.
Buckinghamshire
The official country residence of the Duke of York is The Royal Lodge, Windsor Castle. This is where he mostly lives. He is also entitled to use his official London residence of Buckingham Palace.
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Embassy
The prime minister of England has two locations which are provided for him and his family to live. The official residence in London England is number 10, Downing Street, which is actually several connecting houses, and is also partly offices as well as an apartment for the PM's family. He is also provided with a country house, called Chequers, for breaks from public life. Prime Ministers often also keep their own private homes, which they might have owned before becoming elected, and to which they will return if and when they leave public office, since Ten Downing Street and Chequers are owned by the state, and are only provided for his use during the prime minister's term of office.