This story has pulled on me for some reason...I am not that experienced a researcher, but I'm learning! How sad...I wonder why the "mother" gave up her child....
I have found 13 New Quebec St....it still exists today, right behind Marble Arch....it looks as though it could well be the original building. If you have google earth...zoom in to street view, and click on no. 15....you'll see a place called "The Ritual Rooms"...that is No. 13 New Quebec St.
(You can read about the place here:
http://www.londontown.com/LondonInformation/Leisure/The_Ritual_Rooms/8fac/ )
There are a few options to try and find out the history of this place...you can right to the occupier now...and see how long they've owned it, and what they can tell you about what it was before etc...You can look up the Electoral Roll for this address, and see what it is. I did this for an address in Bromley, and found it to be my great grandfather's barber shop, which I never knew he had!
If the mother really did name her Mona Julia, and registered her birth...the only London registration for a Mona J in 1916, was a Mona J Purdey OND, St Geo H Sq, MMN: MOY. This of course could be a completely different person...AND, the mother may not even have given birth in London to the child!
I will continue digging

Hopefully more experinced people that are better than I will come on board
