The permanent home - Palingswick House - is owned by Hammersmith and Fulham Council.
Three new schools are to open next month in the London Borough of Hammersmith and Fulham.
The "core outbreak area" covers Brent, Ealing, Hammersmith and Fulham, Hounslow, and Richmond.
Hammersmith and Fulham Council will limit tenancies to five years, cutting it to two years for 18 to 25-year-olds.
BBC: Hammersmith and Fulham to fix social housing tenancy term
Other London boroughs with CIZs include Barnet, Hammersmith and Fulham and Camden.
Hammersmith and Fulham Council believes Najat Mostafa lives in the house in Shepherd's Bush, west London, with two of the couple's eight children.
BBC: Abu Hamza wife asked to consider downsizing London home
In contrast to Hammersmith and Fulham Council, Liberal Democrat-led Sutton Council issued its Tenancy Strategy on Monday, "restating its belief in offering open-ended tenancies".
BBC: Hammersmith and Fulham to fix social housing tenancy term
Labour-controlled Hounslow is one of two boroughs - the other being Hammersmith and Fulham- which have announced they will reduce council tax next year.
The document, published in December, added that Camden, Hackney, Hammersmith and Fulham, Islington, Kensington and Chelsea, Tower Hamlets, Westminster, Brent, Hackney and Wandsworth, will become unaffordable.
The Department for Education says the inner London boroughs "likely to qualify" for special funding are Camden, Hammersmith and Fulham, Kensington and Chelsea, Lambeth, Barking and Dagenham, and Haringey.
The Information Commissioner's Office has already obtained undertakings from four other local councils - Hammersmith and Fulham, Islington, Westminster and Wolverhampton - which needed to improve their FOI performance.
The chairman of the Save Hammersmith and Fulham Hospitals campaign, Carlo Nero, said it was about showing there was huge opposition to both the consultation process and the proposals.
One of the boroughs which signed up was Hammersmith and Fulham, and deputy leader Nicholas Botterill said it was essential for firms to complete work in "the most time-efficient manner".
Councils such as Tory-controlled Hammersmith and Fulham in London that are selling off buildings used by charities stand accused of undermining the voluntary activity the Big Society is supposed to encourage.
Hammersmith and Fulham Council said it had suggested the following Sunday or Monday - a Bank Holiday - as alternatives, but the club has said it will make its position clear if it wins Wednesday's final.
He said he was also exploring the possibility of enshrining a "right to move" in law, monitoring pilot schemes in two London boroughs - Kensington and Chelsea and Hammersmith and Fulham - which allow some tenants to ask their social housing landlord to find them a home in an area where they want to live.
BBC: Social tenants in England to get wider home swap choice
Kensington and Chelsea, Islington, Sutton and Hammersmith, and Fulham.
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