The conservation group has been frozen out of talks with developer Parkview International over keeping the stacks.
According to C20, Parkview has decided to reject the society's advice that further testing could lead to a strategy whereby the chimneys could be repaired rather than demolished.
A C20 spokesperson said: 'The society believes that tests ought to be carried out from both the outside and from within the structures.
'Parkview had not commissioned tests from inside the chimneys.
'Their conclusion to replace the chimneys is, in the society's opinion, premature and regrettable.'
The society claimed that any work on the chimneys would set an 'exemplary' precedent for concrete repair in the UK.
The news comes after Ballymore Properties ceased its negotiations with Parkview to take a significant stake in the project.