The heritage quango has approved the City of London's plans to upgrade the tower.
EH said the impact of the proposed changes was 'generally acceptable' and 'will preserve the historic and architectural significance of the building'.
Yet some residents have complained that the proposed changes - including 'improving accessibility to the building' - would impact on the security of the building.
Resident Robert Sykes complained that the removal of white paint would make the building's entrance too dark, and therefore risky for use by elderly residents with poor vision.
The City, advised by architect Peter Inskip, which acts as consultant to the local authority on any ongoing work, has recommended approval for the changes at a meeting to be held on 28 March.
The proposals intend to strip paint in the tower's entrance to return it to its original concrete finish and remove a partition there. The tower was completed in 1976.