My adopted brother was born in 1936. His birth name is recorded on the GRO index and is shown on FreeBMD. Although I believe there is sometimes a note made on this index that the person has been adopted, in his case there is none. The names which he was given by my parents, so his adoptive and legal names, do not appear elsewhere on this index. In order to discover his birth name he had to apply to Kew and receive counselling, after which he was given a copy of his original birth certificate. This was about 5 years ago, so the procedure may have changed since then, of course. The intention was to protect both the birth parents and the adopted child, should either not wish to be traced. At that time if the birth mother wished to contact her child this would be recorded, and if her child discovered his original birth details and expressed a wish to contact his birth mother the two would be put in touch with each other though that office.
I believe that if the adopted person is dead, then only very close relatives will be permitted to receive this information.
Gillg