As i have just removed a stud wall separating our stairs from another
room and now it is an open gap (which we would like to keep this way).
The other wall still exists and has a hand rail.

This is absolutely not acceptable. It may result in severe liability
judgements if a visitor or child is hurt.

There are two issues here, handrails and guarding. You only need 2 handrails
if the stairs are more than 1 metre wide, which is probably not the case.
However, you need guarding if there is a drop greater than 600mm. This is
clearly needed. Generally the guarding would incorporate a handrail. So, in
summary, you can get away with one handrail, but it has to be on the room
side, not the wall side.

The guarding will consist of a handrail at between 900mm and 1000mm from the
tread. Beneath this rail must be guarded such that no object (sphere) of
100mm could be inserted through it. This is to stop babies and children
crawling through and being trapped or falling to their death. The
construction must be difficult to climb for a young child. This basically
means you may not use horizontal rails. You can use vertical banisters,
rails angled with the stair rising, or a solid wall.

Christian.