An investigation to be broadcast tonight also says the council used planning controls to discourage associations building cheap, rented accommodation and instead promoted luxury flats, to help it gain votes.
Nine people who were councillors and officials in the years up to the 1990 local elections have already been found guilty of gerrymandering in an interim report by the district auditor.
But in his report, he only considered policies of selling council houses and moving the homeless to boost the number of Conservative voters at the expense of Labour in eight marginal wards.
Public hearings into the policies, said by the auditor, John Magill, to have cost the local taxpayers pounds 21m, are due to begin on Monday, and are expected to last six weeks.
In a documentary to be broadcast tonight on BBC 2, a former senior official in a housing association will allege that the social engineering went wider than the auditor's investigations so far. On 18 February, housing associations were called to a secret meeting in City Hall, by the then-housing chairman, Peter Hartley, and Paul Hayler, a senior housing official.
Tony Bird, for 11 years the central London manager of the Family Housing Association, told the BBC: 'They made it very clear they wanted associations who had mainly done rented accommodation to concentrate on owner-occupation tenures, and to think creatively about rehousing Westminster households outside the borough for which they would receive borough support.
'It was a very difficult meeting for many people because it was quite a shock. I would say it was bordering on intimidation of the housing associations . . . the crudity of the language and the implied threat of withdrawn support unless they co-operated.'
He said other housing associations had not spoken out because they were dependent on support from local authorities, and they were frightened of losing work.
Simon Milton, current deputy leader of the council, said: 'The council has never been engaged in a policy of social engineering for political purposes. That is not what the council is there for. The council has not done that. None of the statistics, none of the facts,
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