Most sources say it was the 1700 supplement, hence the 1700 date commonly accepted. In any case, Clark wrote Cranbrook as a setting for "While Shepherds Watched", a century after the lyrics were written (or adapted, if you prefer), and that setting preceded "On Ilkley Moor" by about 50 years or more. No news to anyone but the reporters, who may have understood the situation, but did a hash of expressing it clearly.

As for it being the first Church of England hymn or carol to cross from the secular to the spiritual, does this mean that they never sang the Latinate carols, many of which co-opted tunes from folk songs with originally secular texts? Considering how common this practice has been throughout history, I find such a claim rather dubious. For it to be true, the Church would have had to create their hymnal almost from scratch.