"Access to an original birth entry ... applies only to an adopted child over the age of eighteen. In exceptional circumstances (e.g. a court case) if any other person (e.g. a grandchild) wishes to gain access, application should be made not to the Registrar General but to the original court issuing the adoption order or the High Court for a direction under s.50.5 of the Adoption Act 1958. (The Act refers also to the Westminster County Court, but this has changed its name and is therefore excluded from the process.) I have been advised that it is unlikely to be granted for genealogical purposes. An application can be made for any person to acquire information from the full file under the current Magistrates' Rules or High Court Rules, according to where the adoption order was first granted. The clerk of the court will ask a magistrate or judge to authorise the release of information, and although it can be refused there have been plenty of successful applications."
COLIN ROGERS. The Family Tree Detective (3rd ed.) p.36
[Colin Rogers is a Fellow of the Society of Genealogists, and an Associate of the Institute of Population Registration. He runs a consultancy which specialises in tracing missing beneficiaries.]
I hope this helps, and good luck with your search.