Hi Tsu, thanks for that clarification. I can see I still had it a little wrong. But I think Mike has got the family tree correct now.
So it seems we are trying to identify the biological father of Margaret EP's child, and that child is your husband's grandfather. And as Mike has observed, there is no biological connection in the tree so far that explains the match. So it seems that there are two connections between the P family and the H family - the one through the marriage of Jane P and J Calwaladr, and the other via the relationship between Margaret EP and this unknown man. Such linked family trees must be common in small villages in UK.
So as I said before, since the match is 4-6 cousins (and my limited experience with Ancestry suggests 4th or 5th may be most likely), it seems likely that the common ancestor is Hugh H senior's father, perhaps his grandfather or perhaps even Hugh himself. That would mean that the biological father we are looking for is Hugh H senior's grandchild, or his father's, uncle's or aunt's great grandchild. If you know that part of the family tree, you may be able to draw all of these generations and identify everyone who could be the one. You seem to be experienced enough to work all that out.
The tricky bit will then be to work out which of the possibilities is the right one, and that may require some more DNA testing down some of those lines, which may or may not be possible. But if you don't have too many branches in that tree and not too many possible fathers of Margaret P's child, and if some people in those lines are willing to test, then it might be possible to work it out.
There are websites, forums and organisations that specialise in helping with adoptions, and you may find some better advice there, but that is as much as I can understand.
