Thank you for all those ideas.
Ruskie I have a few ideas but I'm not getting anywhere! I discovered early on that my paternal grand father could not possibly have been my grandmother's husband. This came about again via DNA, I have a whole collection of nearish relatives who I had no idea about. After a lot of poking and prodding, my main collaborator (Karen) and I discovered they all had a common surname in their trees. Then, speaking to much older cousins I discovered a potential affair with a neighbour. A check on the 1911 census gave me that same name.
My cM link with those various 2nd and third cousins is nowhere near 351 though. The numbers are a bit illogical, as I can demonstrate. Other than Bernadette (the person in question), these are ALL descendants of the same person, EdA Snr
EdA Snr was the father of LA, EdgA (my likely grandfather), EA, AA and EdA Jnr.
LA was Eileen’s great grandmother
EdgA was apparently my grandfather
AA was Robyn’s great great grandfather
EA was Karen’s great grandfather
LA was Mike’s great grandmother
My DNA shares
Karen 140 (Her link to Bernadette is 364)
Eileen 129
Robyn 107
Bernadette (the unknown) 351
Mike 41 (although he has the same person on BOTH sides of his family
Both Karen and I have approached Bernadette and I've explained things in more detail in a second email. I'm thinking that someone who goes as far as to have a DNA test and then upload it to Ancestry has to have an interest in their family history but we haven't heard back and we wrote three weeks ago. Knowing what we do we just can't see why these various combinations work in the way they do. Karen and I are a generation apart too. I could write to the other "cousins" to see what their link is to Bernadette but I think a reply direct from her might be more enlightening! I can't conclusively find her from an Ancestry search or Google/Facebook etc either...