As a descendant of a Gurney (my mother), I've been doing a bit of family history of the family. Our line comes from Winwick, Northamptonshire but I've been branching out (so to speak) looking at other lines.
The two main ones in the area of the song are centred around Padstow and Dartmouth. Peter does not appear to be a common christian name except for one family; that of Edward Gregory Gurney married, in 1746, Mary Peter and since then Peter is used quite often as a second christian name (in fact, one of Edward Gregory and Mary's sons was Thomas Peter Gurney, but known as Peter).
That, in a roundabout way, is me saying I can't offer any new information to this topic but if I do find a Peter who fits the bill, I'll let you know!