From the Building Regulation approved docs, top of stair handrail to be min 900, max 1000 above string line of the stair, anywhere it forms guarding i.e landings, balconies, balustrades, to be 1100mm above finished floor level.
Handrail diameter to be between 40 and 45mm.
Had a drawing from an Architect before xmas showing handrail heights on a stair at 1100 high. You'd think they would know better...