The order is quite clear- the hirer becomes a temporary responsible person and is responsible for basic fire precautions for their event in so far as they have control. The Committee/overall RP have a duty to coordinate and communicate.
Where there is no supervision by the committee or premises supervisor, i usually put together a one page tick box checksheet for the hirer to be issued and briefed as part of the conditions of hire that sets out the basic fire plan and essential information for the premises.
The hirer then signs all boxes to show understanding and undertakes to carry out the supervisory duties during the event- controlling numbers, keeping exits clear, briefing visitors, controlling noise levels, nominating competent assistants,implementing the emergency procedures, looking after persons with special needs safe shutdown at end etc.