I think there is - my parents have open stairs (no banister) and were told if they wanted to sell the house they would have to put one up.
"Approved Document K of the Building Regulations 1992 states that:
Private stairs the maximum rise should be 220mm, with a maximum pitch of 42 degrees
Flights of stairs should at least have a banister on one side if they are less than a metre wide, and a banister on both sides if they are wider than a metre. The bottom two steps of the stairs do not require a banister
The minimum height of the banister is 900mm for stairs and landings
Balustrades and spindles should have a gap between them narrower than 100mm
In the UK, staircases commonly comprise 13 rises."
from here