The local authority originally backed a conservation area designation which would have saved Potter and Hare's 1962 building, but has now changed its mind.
The Church of England, which owns the building and is planning to replace it, has already sold a second site in the neighbourhood in order to finance the church's destruction and a replacement scheme.
Conservation group the Twentieth Century Society has launched a campaign to save the building, describing St Mary's as 'an impressive, well-designed building which is structurally sound'. The group also said that destruction of the church would be 'an act of vandalism'.
The society added that replacement designs are of 'no architectural merit' and would spoil what is otherwise an architecturally rich street.
St Mary's Road, where the church currently sits, is also home to the Grade II*-listed Pioneer Health Centre by Maxwell Fry.