Wow, Gary! I just read your amazing story! I have 3 adopted children myself, but their parentage is known. I cannot imagine what you are dealing with. I understand very well that my children's history is their own and respect their wishes if they some day pursue a relationship with their biological families (my middle son's paternal grandmother is a big part of our lives to this day and she is "grandma" to all 3 of my kids!)
I was wondering if you have tried a search of birth certificates in the UK region during the 2 weeks prior to your birth. Unless your mother gave birth to you all on her own, I would imagine that a birth certificate might have been generated or some record of your birth at a hospital. I would have no idea of how many births that would entail, but would imagine that all of the other records are searchable for future applications for social security numbers (or the equivalent in the UK,) school records, death records, etc...to match up at perhaps narrow down your search somewhat. While it sounds like a big job, perhaps one of these resources you are working with can help you with the costs, such as the Guardian.
Another clue would be that your mother was likely very young, as she was apparently still living with her parents at the time and feared her father. She was also unwed, obviously, so that would limit the scope as well.
Also, it is very unlikely that she did this alone. Someone must have assisted with your birth and early care. If she was living at home, there isn't a way she could have hid your existence in the home for up to 10 days! Someone heard you cry. Someone else must have seen you, so keep trying, as I hardly believe she would have been the only person on earth that knew of your existence.
As far as your belongings that were left with you-is there any way of finding out where they were purchased? Often times, the manufaturer of clothing items can look at the garment/tags and determine where these were sold and during which times. Was a cheap garment or perhaps one that would indicate better financial circumstances?
You may also wish to have the garment tested for DNA. I'm not sure if it was used and washed after you were found, but perhaps your mother left some DNA behind-maybe some tears, a kiss, fingerprints, etc... You never know. If she has ever been arrested you might find a match or even if a sibling or other family member, you never know.
Also, you should keep in mind that your mother may have already very well heard your story and cannot come forward for whatever reason. Perhaps the next time you send out a story, suggest she send an anonymous letter to you that would simply let you know that she has heard your story.
Whatever the case, you have a wonderful gift of knowing that she loved you, cared for you and probably watched very closely to insure you were found safely. My heart breaks for her, but she gave you a very selfless gift of life, like you said. Treasure it and enjoy it whatever the outcome of your search.
I wish you the best of luck!