Intriguing and emotional story this one. It's a hard period this to research in as so much is not available on line.
One of the main problems from what I understand on adoption cases, having worked on a few, even those that were not formally arranged through solicitors, is that birth parents could and did change around the information so the real facts woud be harder to trace. Names can be the other way around, dates near but slightly out etc.
I spent some time on this yesterday and found one potential family where so much could have fitted (this is the one I sent you details on yesterday Marty) but this morning I found an 1938 marriage for the potential daughter I thought might be Mona, so I think I can draw a big line on that group

So where are we now? Kathy, you have emailed the Portman Estate on background on 13 New Quebec Street for that period, so lets see what comes back on that. You have also ordered a couple of certificates as potential entries. Again, let's see what is on them and how we can move from there.
I agree with all the comments on the letters. I do not think that Mrs A T Scott was a business woman more likely an employee, from her letters: “ I find that I can find more time than I expected” and “you see, I shall have to lose time from business”. She is sounding to me more like she was employed rather than in charge and arranging time off work unexpectedly but worried about taking any more time off.
Hopefully some new clue may be revealed.
Monica