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You will find the answer in BS 5395 part 2 but it will not tell you the actual diameter required for a spiral staircase. The standard specifies the clear width required for different applications. For instance spiral staircases serving as the main house staircase would come under category B which requires a clear width of 800mm.
The definition of the clear width is the distance between the outside of the spiral stair centre pole and the inside of the handrail, this in practical terms is the width that you have available to walk up or down the stair. This is a good way of specifying the required size because if you have to escape down it in the event of a fire this width could be critical. Specifying the outside diameter of a spiral staircase does not really define the clear width because different designs and different styles have different sized centre poles and handrails which will in turn have change the amount of clear width.
None of the above really helps the questioner, what he really wants to know is how much area he needs to leave to accommodate a compliant primary spiral staircase in his new house design. The answer is about 2000 mm diameter, I say about because as you now know, without knowing the constructional details of a the specific spiral stair I cannot say for certain. Personally for design purposes I would leave if possible an area 2100mm square this would just about cover most models of spiral staircase that you are likely to buy. In my experience I have not found any modern designs of Category B compliant spiral stairs that are smaller than around 1900mm.
The only real safe way of answering this question is for you to choose your spiral stair model and ask the manufacturer what diameter will comply under BS 5395 part 2 as a main staircase in a dwelling.
The spiral staircase Doctor.