i doubt it but as regulations vary from place to place check with your local planning office to be safe. it would be false economy not to.
your,re building this yourself or is it a kit?
In my copy of building regs it refers to British Standards BS585: Wood stairs part one and BS5395 Stairs part two design of spiral stairs.
Wonder if you would need building approval. Suggest consult council planning as very helpful and can ask without being interrogated!