The organisations hiring the premises would be well advised to have some insurance cover of their own, although there is no reason why the village hall committee should insist on this. (The hirers may already have appropriate insurance to cover all of their activities, irrespective of location, anyway).
Two examples to explain what I mean:
Case 1: A visitor to an art exhibition suffers an injury when he stumbles on a step inside the building. The step was in a poor state of repair and the area was inadequately lit. It's clear that the hall committee should have identified the safety hazard, so the injured person sues the committee (and, ultimately, their insurers).
Case 2: A visitor to an art exhibition suffers an injury when he trips over a cable providing the power to spotlights attached to one of the display boards. The boards and lights were put in place by members of the art club. It is the art club which should have identified the potential trip hazard so it is the art club (and, ultimately, their insurers) which will be sued.
Chris