Agree with redone: in a premises which is one of several occupied by an organisation, there can be multiple 'responsible persons'. For exammple, a local manager may only be able to authorise a payment of, say, £1000, which may not be enough to cover any alterations to the fire alarm determined by the risk assessment, so it may be a person further up the ladder. But that person may be responsible for the running of several premises, so may not be reasonable for them to check that all fire exits are available and usable, so the local manager would be responsible..
What an organisation needs is well written contracts and job descriptions that clearly set out what that person's responsiblities are. I've been to so many places where the task of completing a risk assessment is handed down to the person at the bottom of the ladder who has no-one else to pass the buck to. They have no training, an no autorisation to make any changes to the management or structure of the building, so the risk assessment becomes a pointless paper exercise.