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They are in the Transcripts of Various Memorials, rather than the Index of Parish Transcripts.

I have just logged in to our site and was able to access the Churchill MIs.

sorry cannot access transcripts!

Thank you both for taking the time to look at this. I think that Pat is probably right and that Mary HALL was the child in question. But I will obtain a copy of the Bastardy Order just to be sure.

As regards George Ford HILL of Cheddar it looks like he married Hannah BANWELL in Cheddar in 1843, so unfortunately this not "my" George HILL.

The search continues.

I had assumed that any child of the single woman, Ann HALL would have the surname HALL.  The Winscombe Baptisms for 1 May 1814 have the christening of a 4 year old Mary HALL base born daughter of Ann HALL who could be the daughter of the George HILL who was mentioned in the document.

"a child to be born of Ann Hall". I meant the child not the father.