Saudi,
This would be a major development, and may not be possible while the apartments are occupied.
The weight of the extra floor would have to be carried down through all the extra floors so depending on the construction of the apartment block , it may necesitate strengthening columns on all the floors below to carry the extra weight. The other work to provide the services (electricity, water, sewerage, etc) would have to go through the floor below. The stairs (and lift if applicable) would have to be extended.
Additional fireproofing may be needed on the current top floor.
All these would have to be considered, so it certainly is possible to do this, but not without major disruption.
I may be wrong, but i think the Iveagh Flats were undergoing a major refurb and would all have been unoccupied at the time anyway.
The only way you are going to know if it is possible is to get a structural engineer to examine the current building and do a feasability study on the cost etc of the project. It may not pay for the inconvenience to all the current residents.