Ah - you have confirmed my suspicions, and I am fascinated by your lateral thinking re the census returns

I actually discovered this link through DNA testing! I am descended from the Whittlebury Linnells via William's father, another William, who married Elizabeth Elliot of Luffield Abbey in 1790. I have several Whitlock DNA matches, but no known Whitlock ancestry, and Ruth Whitlock having an 'out-of-wedlock' child with William Linnell (of whom there were several possible candidates..) seemed the most likely situation. Whittlebury Parish Registers have:
"Rebecca daughter of Ruth Whitlock, baseborn, born 21 Sep 1811, bapt Oct 20 1811"
Rebecca married a William Braggins, and after he died, she joined her eldest son in emigrating to the USA. Her Pennsylvania death cert gives her father as William Linnell, so her paternity was clearly widely known within the family.
Rebecca was born before William married Hannah Adams (who was his cousin, John Linnell's widow)
I wonder who the father of her second child was?!
Many thanks for this clever sleuthing.
Joan