Agreed, that's what I was saying. Part K (as a publication) applies to all buildings, but as you mentioned, there are sections within which refer to various building types. A block of flats/apartments is not classed as a dwelling, but the units within it are classed as dwellings. Therefore 1.18 refers to the circulation space within (and outside) the building (but not within the dwellings themselves) and which I needed clarification on.
For circulation spaces in the communal areas as you propose up to 12 steps then a half landing then another flight is completely fine and standard practice.