The paragraph about "current public entertainment licensing law" and the Church of England is bringing out the point that the present law (ie before the Bill going through Parliament becomes law) is highly discriminatory against most places of worship, which of course are not C of E. The new law will not make this distinction, they say, it'll apply on the same basis to churches of all denominations, chapels, meeting houses, mosques, synagogues and temples. (Would Stonehenge count?)

I suspect it'll end up on the same basis as council tax - if it's a place of worship for council tax purposes, it'll be a place of worship for licensing purposes.