Chrissie
I suspect the answer is you won't be able to find this information from any official source as the time-scale suggests it would have been a private adoption. There is a bit on the government family records site:
http://www.familyrecords.gov.uk/topics/adoption.htm
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Adoption
Legal adoption was introduced in the United Kingdom in the first half of the twentieth century. Earlier records of private arrangements can be very difficult to trace.
What information is available?
Please note that only the adoptee is allowed to apply to see their original birth records and to go on the Adoption Contact Register. Unfortunately for family historians, this might mean that you will not be able to trace your genetic line, if you discover that a parent or grandparent was adopted."