I just can't shake this feeling of needing to solve the mystery though!
I can understand that. In my case I've been thinking about it for over 20 years, but still don't feel any closer to the truth. My last try was to get hold of the wills of some possible candidates to see if any had left money to the people concerned. No luck there.
I get the sense that she never told anyone because he wasn't around anymore and she loved her step dad as her father, but perhaps a feeling of sentimentality came over her that one day in the graveyard.
That is plausible, and a reason to ask people not to investigate might be a sense of loyalty to her step dad. It gets complicated without any documented information. It is also important to avoid making assumptions that block possible avenues of investigation.
David Thomas Hughes her stepdad lived about 30 or 40 miles away from Wem, where her biological father is supposedly buried. I think she went so far because it was the nearest workhouse.
Bear in mind that by 1935 a 'workhouse' is more like a hospital than the kind of institution Oliver Twist would have known. Have you looked into the history of this place, what status it had in 1935, and what happened to their records?
Do you know how long she was there after the birth, and what happened between then and her marriage? What she was doing in that time might give some clues as to who the father might be. It is a long shot, but as an example she might have lived with/worked for some family member of the father.
What reason do you suggest for exploring his history, do you think he could actually be the biological father?
The suggestion was because it may provide a source of clues. It is a case of turning over all the stones looking for possible connections. That's based on my own experience where I've followed up a loose end like this and discovered something interesting - even if not the exact answer I was looking for.
To give an example, say you discover a relative of David Thomas Hughes living near Wem working as a farm labourer some time pre-1935. You might then want to look at the farmer they were employed by and see whether that might fit the circumstances you've been told. I'm not suggesting this is a likely outcome, just an example of how sometimes a clue can come from an unexpected source. The problem you'll have though is the limited records available between 1911 and 1935.
Based on the information you've given so far it sounds improbable he is the biological father, but equally there is nothing so far that would absolutely rule it out.
But on balance if he was the father then it might be more likely that the circumstances of the birth would have been glossed over and as far as your grandmother was concerned he would be her dad without any doubt.
