Is it legal in England to use voice amplification to communicate (without specific notification) religious rites (on a day significant to that group) such that it is audible to hundreds of domestic properties in the vicinity?
Religious rites have no specific significance in English law, and it may be that this broadcast is committing a nuisance; you should contact the local council for more details on how to complain. However, there seems to be a contradiction between 'without prior notification' and 'on a day significant to that group'. You can expect church bells to be rung on Sundays, just as you can expect farms to be busy and noisy around harvest; your right to quiet enjoyment does not prevent others using their property as it should be used.
If this religious organization wishes to mark a particular day by a broadcast for the first time, it is a matter for an Environmental Health Officer to balance their rights with those of the other residents, which will not be a simple matter and could potentially end up in court. If this has happened before, presumably the decision permitted the broadcast (possibly with some restrictions); it can only be changed by the council or by judicial review.