The council argues transferring families is logical as its land and property prices are the highest in the country, and that the same money can build more homes elsewhere.
Its approach has been fiercely criticised by one council, Hammersmith and Fulham, which blames Westminster's council house sales policy
for the shortage of accommodation.
Earlier this year Conservative-controlled Westminster was accused of selling council properties to people other than sitting tenants to increase the Tory vote in marginal wards.
The policy was suspended after a preliminary report by John Magill, the district auditor, denounced it as 'disgraceful, unlawful and unauthorised. However, last month councillors voted to resume the sales with 140 properties being marketed in the first year.
While Conservative councillors claimed the policy bore no resemblance to that criticised by the district auditor, Labour argued that it was identical in all but name.
Funding for the kind of 'out of borough developments suggested by Westminster is available from the Housing Corporation, as long as both boroughs agree to the scheme.
Earlier this month Janet Prendiville, Westminster's housing initiatives manager, wrote to Hammersmith's director of housing, Barry Simons,
to seek such consent. In her letter Ms Prendiville states the city council has to find at least 300 new family homes a year. She claims that a shortage of land and high prices 'make large areas of Westminster not viable for housing association development.
In his reply, Mr Simons describes himself as 'surprised and, I might add, annoyed' by the request. 'It would appear that the City of Westminster has consistently attempted to reduce the amount of lettings available for priority-need households within its own stock by its sales policy. It is, therefore, totally inconsistent, in my view, for Westminster to seek the co-operation of other boroughs whilst this policy continues.'
Iain Coleman, leader of Hammersmith and Fulham council, was 'staggered' by Westminster's request. 'Having sold off their public housing stock for political gain they are now finding it impossible to meet their obligations to homeless people.
'They will have to think again if they imagine that they can get out of this mess by shipping their homeless families into our borough.'
Westminster said: 'We are disappointed by Hammersmith and Fulham's negative attitude to what we thought was a reasonable request.'