One of the problems with churches (and other charities) is that the HSE likes volunteers to be treated as if they were paid staff as far as H&S is concerned. Most churches have more than 5 volunteers and I always recommend that they do record their significant findings and where necessary act on them if shortcomings are found.
As far as training goes, a short summary of what people ought to do needs to be provided either in writing or verbally. Where people have specific duties - for example as 'fire wardens', then I think they should always be given written instructions specific to the building(s) they work in and a record kept of this training.
Additional comment:
Most churches are 'places of employment' as well as 'places of public assembly'. While in the Anglican church most clergy are classified as 'self-employed', in other denominations the clergy are often employed by a church group or committee. There are also other employees such as organists, possibly cleaners, and in larger churches there may be paid secretaries, shop staff etc.