The world-class arts centre was this week criticised by the Commons Culture committee as chairman Elliott Bernerd resigned.
Lambeth Council had sat for more than two years on a "simple, non-controversial planning decision" to renovate the Royal Festival Hall, and the delay was putting the £212m project in jeopardy, the Commons Culture committee was told.
The complex is already without a chief executive after Karsten Witt departed last year. In an unrelated twist last night Elliott Bernerd, the South Bank chairman, who has is suffering from cancer, announced his resignation.
Lambeth will hold another meeting on the South Bank plans next month.