Neil
The way I was traced was that my daughter and her adoptive father, used her birth certificate to find my name. From that they looked for a marriage and also my birth, just to check that they had the correct marriage as both give father's names. I suppose if I'd been illegitimate too, that might not have worked.
Having found my married name they then searched for any children I might have had, as you can search for a birth of say Smith, and quote the mother's maiden name, say Brown for all births from 1912 onwards. Having found the very last child, they wrote to the address on the birth certificate in case we were still there. We weren't as we tend to move around with my husband's work. The people in the house were very helpful and said where they thought we'd moved to, but we couldn't be found there either - of course we'd already moved. Eventually, my daughter's adoptive father (Mr M) decided to search through electoral rolls to see if he could find me and my husband but he said there were too many with our names, so he thought he'd look for our children (well our sons anyway) to see if that was easier. Fortunately one of our sons is called Guy, and there were only 4 of that name and our surname in the electoral rolls. Mr M decided to ring each one, but struck lucky first time. He just told our son that he was doing family research and that he thought he had a connection with my family. He gave my son my name and his dad's name, plus the names of his siblings to show he knew what he was talking about. My son gave him my 'phone number but said we were moving soon. However, they looked us up in the 'phone book, we're not x-directory, to find my address. Then my daughter wrote a letter to me, on the lines of that she knew me many years ago in 1960 and would like to get in touch again, so that if anyone else saw it, it wouldn't mean anything to them.
Of course, I'd not told anyone about my first daughter, not even my husband, but I wrote back to her and said I'd have to tell my family. It took me about a year to pluck up courage, but my husband was wonderful and just said "When are we going to see her then". My sons were all happy for me and one of my sons and his wife have met my daughter. However, my daughter with my husband was not happy and doesn't want to know anything about her.
My daughter's adoptive parents said that from the day they picked her up from Doriscourt, they were adamant that one day they would find me, as they felt that the happiness they'd got was outweighed by the sadness I must have felt. I've actually met them more than my daughter, as she doesn't live in the UK, and they are always so grateful that I gave them my daughter - of course I didn't know who she was going to.
Hopefully, you might be able to trace your birth mother using the methods Mr M used. In fact he did most of the searching as he lives in UK and is retired and he had to spend hours in the library looking through electoral rolls, and I guess BMDs as he didn't have a PC at the time.
Good luck - but tread carefully if you do find your birth mother as you might be her secret. Just write her a letter saying that you knew each other in (whatever year you were born) and that you'd like to get in touch with her again. You could even sign the letter with the name she gave you so that she'd know who you were. Be ready for the fact that she may not want to have any contact with you though.
Lizzie