Maybe I didn't explain myself too well. I don't 'know' that my Henry BOULTER was born on this date, or that his mother was 'Anne'. I have come to a brickwall, and I realise that this is just a 'stab in the dark'. It fits with the dates though, so I am wondering (but am by no means certain) if this Henry (the one married to Anne Holloway) could be his parents.
I found seven children of Henry (and all, except No. 4, Henry, have a mother called 'Anne'). My Henry slots in there very nicely, so it is possible, and it is also possible that the mother's name of 'Mary' could have been an error on the parish register.
1. Millicent, b. abt. 1767, Potterne (parents: Henry & Anne)
2. Gabriel, b. abt. 1769, Potterne (parents: Henry & Anne)
3. Mary, b. abt. 1771, Potterne (parents: Henry & Anne)
4. Henry, b. abt. 1774, Potterne (parents: Henry & Mary)
5. Jemimah, b. abt. 1777, Potterne (parents: Henry & Anne)
6. Richard, b. abt. 1781, Chippenham (parents: Harry & Anne)
7. Ann, b. abt. 1793, Chippenham (parents: Harry & Anne)
I have found no other Henry BOULTERs in Wiltshire that come anywhere close to these dates. As I am in Australia, I can rely only on what I can find through Ancestry or elsewhere online.
I was hopeful that somebody may be researching the same family and have other information.