Wiltshire Parish Records

[Phoenix]

My ancestor John Horne lost his wife Mary in 1738/9, just after the birth of their son John. Mary was buried in South Newton, Wilts.

John's next known child, Mary, was bp in South Newton 13 March 1742/3. Mary's mother is Anne.

They had another three children:
another John 1745
Robert 1748
Nehemiah (not a known family name) 1751

So, if a marriage took place, it was some time between 1739 and 1742.

And there is a marriage that fits the bill:

John Horn m Ann Miller 28 Jun 1739 Orcheston St Mary, Wiltshire, England

Unfortunately, this is a transcript. I cannot find the register on Ancestry.
Nor can I find any information about the parish registers.

It would make perfect sense that John, with an unweaned child on his hands, remarries very quickly. However, I would like to see the proof.

Genuki is no help, and Wiltshire & Swindon Archives only mention Orcheston St George.

Can anyone suggest where the records might be? It seems unlikely that they would still be held in the parish.