The embattled local authority has withdrawn the housing land supply arguments from its evidence in appeal hearings into two applications in Brereton and Sandbach.
A council spokesman said: "At a meeting of the Strategic Planning Board on 15 November, the council decided not to present any further evidence on housing land supply on two ongoing planning appeals, at Rose Cottages in Brereton and Waterworks House in Sandbach.
"Both these appeals have already heard evidence on other grounds, such as sustainability and ecology, and were due to be reconvened to hear further evidence on housing land supply.
"In the light of recent appeal decisions which indicated the council could not demonstrate a five-year supply of housing land, it was concluded that there was little merit in pursuing this aspect of the case any further.
"Both appeals will continue to be opposed but on matters unrelated to housing supply."
Bloor Homes proposes 25 homes at Rose Cottages. The council refused planning in December 2012; the appeal began in October.
The Waterworks Trust plans to build 12 houses on the site of Waterworks House in Sandbach.