Wiktionary
n. (context British as a modifier to a form of accomodation English) Owned by the sovereign or government and granted free of rent to a person as an expression of gratitude or obligation.
Wikipedia
A grace and favour home is a residential property owned by a monarch by virtue of his or her position as head of state and leased, rent-free, to persons as part of an employment package or in gratitude for past services rendered. Some are owned by UK charitable trusts.
It is possible that the term crept into English through the writings of Niccolò Machiavelli, who wrote of advisers who are ministers per grazia e concessione, which has been translated as "through grace and favour".
In the United Kingdom, these homes are owned by The Crown or a charity and, in modern times, are often within the gift of the Prime Minister. Most of these properties are taxed as a "benefit in kind", although this status does not apply to 10 Downing Street or any home granted for security purposes, such as the residence of the Secretary of State for Northern Ireland. They are at times granted to senior politicians.