Enquirer was visiting a Head Office of a large company and was approached on two separate occasions by two different members of staff within the hour and was politely 'told off' on the grounds of Health and Safety for:
1) not holding the hand rail when ascending the stairs
2) talking on his mobile phone whilst descending the stairs
The building is very modern and the staircase large, not steep and is open plan.
Whilst it is true that slips and trips on stairs are a common cause of injuries at work, there is no mandatory requirement to "hold the handrails" Research actually suggests that the key requirement is for handrails to be available, visible, and at the right height so that they can be grasped in the event of a slip or trip rather than be continuously held. Given that people need to be able to recover themselves in the event of a trip on the stairs it is probably not a good idea to be using a mobile phone.
There are no specific legal requirements on either of these matters, so it would have been preferable to point out that it is company policy rather than the catch-all "health and safety".