Thanks for your help. I think I've gone about as far as I can go with this link. As I understand it Henry Dennis and Sarah Burn had two children baptised on 4 August 1754: Thomas and one unnamed, who was presumably the weaker of twins and thought unlikely to survive. One did die in his first year and the surviving child was named William, who turned out to be my 4x gt grandfather. I think Henry's parents were John and Dorothy (and hence Thomas 1660) and Henry's brother John married Eleanor Dodge.
The name Burn is sometimes spellt Bourn(e), which has a more English Midlands ring, but the derivation appears the same and, bearing in mind the influence of the Danelaw in earlier times, I wonder if the scribes were responding to a more northern pronunciation.
Happy New Year!