The heritage quango was obliged to drop its objections to the cleaning process after it emerged that there was a possibility that parts of the render may be about to crumble onto the pavement below.
The process of returning the building to its original state has now started on site.
Whether to remove the thick layer of dirt or not has been a highly contentious issue within the club, which is frequented by many of the leading lights from the arts and media worlds.
The Italianate building, which was completed in 1872 by Frederick Marrable, is known to have one of the very few unpainted renders in London.
Now that investigations have concluded that this render is in danger of disintegrating, the club has commissioned London-based Richard Griffiths Architects to undertake the work.
'There was a very real concern that some of the render was in trouble,' director Iftikhar Kahn told the AJ. 'You don't really want bits of it falling down on to the pavement, do you?'
'English Heritage and Westminster council were opposed some time ago but they were forced to change their minds when support for the cleaning process was gathering support.
'It was the heath and safety issues that won the day,' he added. 'They outweighed any concerns over whether the project should go ahead or not.'
The scheme is scheduled to complete in September.