The rules for stairs are quite prescriptive and depend upon the use they serving.
Please see the following guidance:
S3.4 The width of a stair, measured between handrails and clear of obstructions, must be at least 1 metre, except -
a. the width of a private stair may reduce to at least -
i. 900mm where it is within the accessible storey, or ii. 600mm where it serves only sanitary accommodation and/or one room, other than a living room or kitchen, or iii. 800mm elsewhere; and
b. stringers and newels may each project not more than 30mm into the width; and
c. a stair lift projecting into the width may be fitted to a stair within a dwelling.
Note::
There are additional stair width requirements for escape stairs in Part E.