My relatives adopted a mixed girl in the 1960s. As far as I'm aware their daughter has never been able to trace her family, I'm not 100 % sure. They weren't especially naice or rich or anything - but they are Catholic and so it might have been done via the church. DM thinks it was (and has been for a couple of centuries) quite common in Catholic Church to adopt.
That said, I also have my fathers adoption papers from the late 50s (58) via Church of Scotland. On all papers (I have from the initial enquiry to letters discussing a sister) it was fully specified what race your possible child was. At that stage they were just sent a letter saying, 'I have baby Julia who I feel will be good for you. Julia is white with fair hair. Mother is white as is father.' So it must have been very important for a lot of people.
It's amazing how different it all is now - I have a record of where my father was born (mum and baby home), and a spiel of false information. It details his mother as being 26 and father as having xyz job. Mother was 17, father was either paying her or raped her i.e. little or no chance that she knew his occupation! All very odd. The church did hold records - accurate ones - but the parents never got them. Dad had to search himself when old enough, thankfully having been told he was adopted. I know in Carole's case it would be different - she'd know - but it must be often a bit of a futile nightmare trying to search for records.
In contrast when my aunt adopted two children (siblings, three years apart) they had regular visits, met the mother, have full contact details for the mother and siblings, children received contact for some time (cards), the eldest (who was old enough to remember her mum) was sent with a photograph album and both have scrapbooks. Just so much better.
I wish that Shelagh had kept her though, I was on the edge of my seat hoping.