Julian's Hymnology seems to confirm that it is William Drummond that we are looking at. There is a surprisingly wide variety of hymnodists and psalmodists represented in The Divine Companion. I suspect that the texts were chosen by the composers from whom he commissioned straightforward settings, rather than by Henry himself.
Well now we know the two names appear in 1701, I can only proffer William Drummond of Hawthornden 1585-1649. His translation of St Ambrose`s 4th century hymn appears in RCH (No 4): O Trinity, O... more
It seems Drummond mostly wrote on non-spiritual themes, but some poems with Christian content are in his Urania collection. Maybe you could find your Playford text in this, or via the indexes of... more