Stairs in dwellings are governed by Part K of the building regulations, with guidance in Technical Guidance Document K covering rise and going, pitch, headroom, width, landings, handrails and guarding. The specific dimensional limits should be taken from the current TGD K rather than from general rules of thumb.
Part K sets out requirements so that stairways, ladders, ramps and guards are safe to use. For a private dwelling, the guidance addresses the relationship between the rise and going of each step, consistency between steps in a flight, minimum headroom, landings at the top and bottom, handrail provision and the guarding of drops.
Alternating tread stairs and steeper arrangements are permitted only in limited circumstances described in the guidance, which is often relevant in attic conversions where space is tight. Designing the stair early, rather than fitting it in later, usually avoids compliance problems.