My sister and I each read this as a hardback (Oxford??) library book. I read it in the 1970s when I was in early secondary school, and it felt pretty recent and ‘realistic’ at the time. It was definitely set in the UK.

SPOILERS. The girl overhears her mother speaking. The girl has recently misbehaved in some way and she hears her mother criticise her and say that she’s just like her ‘real mother’. She’s discovering that she’s adopted, and her adoptive mother knows her biological mother.

Eventually the girl discovers that her mother’s younger sister is her biological mother.

The girl is upset by the discovery but is helped by her grandmother, as their relationship hasn’t changed.

The aunt/birth mother had babysat the adopted girl and her sister when they were babies. The adoptive mother reminisces about how, when the aunt/birth mother babysat, the adopted girl missed the adoptive mother much more than the other child had.