I think I've solved this one!

It always pays to look at records on more than one site, wherever possible. The transcription of baptism records on this site shows a William Trigg baptised 6 April 1766 to parents Richard and Elizabeth, and then another William Trigg baptised 4 May 1766 to parents William and Mary. Having looked at Ancestry and Familysearch I now see that the surname for the first of these baptisms is not for a William Trigg but for a William Ridon/Rider. Looking at the original it's clear that the only William Trigg baptism is 4 May ... and therefore his parents must be William and Mary.

Obviously I'd still love to hear from anyone else researching this family - there's lots still to unravel.