Many thanks to you both for offering some support with this. I have re-covered my research as we had some differences, which I hope I can clear here.
William Belcher married Mary Baughan, a widow 13 Jun 1767 at Heyford at Bridge - Heyford Bridge and Heyford Lower appear to be the same place. She was a widow having married William Baughan at Heyford at the Bridge 17 Dec 1756. Her maiden name was Coulling, a surname which can have many spellings! Both parish records are available to view online. William Baughan was buried 30 May 1766, Heyford Lower, again the parish record is online.
There were children to the Baughan marriage, William, Mary, Thomas, Stephen, James and John. All baptised at Heyford Lower. … and children to the Belcher Marriage, as you have them Teresa, with the exception of John, who was born before Wm Baughan died, so we kindly assume he was his child.
My husband is also a direct decendant of Stephen, via his daughter Hannah.
Colc, you would be correct regards Mary Coulling - I found a good birth record at Tackley -(Tackley is 2-3 miles from Heyford Lower. Surname is written as Cocking) “parents Abel and Mary his wife”.
Still no sign of Williams parents.