What is interesting is that the south Tower was demolished first but quite clearly in this photo it is still standing fully. So this photo was of some early work before they dynamited it.
I've got that one; it's a press photograph with no date. On the back it says:
Famous Landmarks to Feed the Guns
Starting the work of demolishing the towers of the Crystal Palace, which will provide thousands of tons of scrap iron. The picture was taken from the top of one of the towers, and shows the other in the distance
Copyright photo issued by Central Press Photos Ltd... Fleet Street.
I've uploaded the picture here.
It has been suggested that the men were merely posing for the photograph, and it certainly looks like it, although I suppose they might have been recovering material (lead, perhaps) before demolition took place.