I wrote a long reply to this the other day, sorry - I think I forgot to post.
DNA may be your only way forward, if at all. My grandma was adopted (pre 1927 so no records before then) but hers was a complicated situation, unmarried parents who split and went their separate ways and simply left the children. At least their births were registered. There was possibly one other brother that 'may' have been related (no birth registration) but as he didn't have children there are no descendants and impossible to prove through DNA route. I am still trying to find out the exact circumstances surrounding my grandma's adoption. My aunt was also adopted, father unknown.
I do have several other incidences of adoption in the family, and these were nearly all unmarried mothers. Look closely at the birth dates of cousins and siblings within the family. Do they tally? Was one child really that premature a birth? My grandmother's sister was brought up by their uncle and his wife, as their own... however, while she and her uncle's daughter were born consecutive years, their 'mother' could not have given birth to them both naturally. My great grandmother from another line had an illegitimate child who was brought up as her brother by her parents and baptised as their own - there was an instance of this in my husband's family as well. Also, his great grandmother died in childbirth from a haemorrhage, which left me wondering if the baby had survived at all - in fact she had been taken under the wing of her paternal aunt and her husband, given their name and brought up in a different part of the country, but... her birth month fitted in. Look at neighbours too. ('39 register).
I've been researching my grandmother's early life for many years. People tended to keep very quiet about such things and my grandma took a lot of secrets to her grave.
