Proposals that have been lodged with City of London planners, who are recommending approval, would involve losing one of the 'pivotal features' of the original design.
Only two examples of unglazed roof terraces remain in the Wallside area of the complex - and one of them is now under threat.
The application has triggered the latest row over the future of the buildings, which are considered one of the finest examples of 1960s architecture in the capital.
The planners that want the changes to go ahead argue that the majority of the roof terraces have already been altered.
However, this argument does not wash with local objector John Greager. 'On the contrary, that is precisely why retention is necessary,' he wrote in a letter to the Corporation dated 24 October.
'The fact that people move into the Barbican, and then seek to alter their environment by expanding it into something for which it was not designed, is not something which, on any reasonable view, should be encouraged,' he continues.
The application would see the enclosure of a section of roof terrace with glazed timber-framed sliding doors.