The group has demanded that Westminster City Council reconsider the proposed demolition of Imperial College's Southside Halls of Residence in Kensington, designed by Sheppard Robson.
The move follows an investigation by engineer Alan Conisbee and Associates. In its report, the firm criticises claims by rival engineer Adams Kara Taylor concerning the building's structural integrity.
Twentieth Century Society casework officer Eva Branscombe said: 'The reason we didn't object originally was that we thought the building was beyond repair. But this report says the problems can be fixed.'
Alan Conisbee and Associates was instructed by local residents to investigate the structural condition of the 1963 Southside block.
The engineer's report says Adams Kara Taylor's original report would mislead, in particular over claims that '70 per cent of the mullion panels to the Southside building are defective with 60 per cent of the spandrel panels showing cracks and twists'.
Conisbee's report concludes that few of the building's defects have structural significance and could easily be restored.
The society has called on the City of Westminster to 'seriously review this new evidence'. In a letter last week, Branscombe said: 'It is an excellent building that should be saved and restored if at all possible.'
Adams Kara Taylor director Albert Taylor, who advised Imperial College on its planning application, said: 'We went through a long consultation process prior to submitting an application. If you go and see the building, many of the issues are plain to see.'
In late January the council approved demolition of Southside and construction of a new scheme by Kohn Pedersen Fox.