Hi Phil ,what you say about permission for your baby to be adopted is true but every baby has to be registered by its birth parents/parent and that record is still on the GRO records for ever and the birth certificate is available to whoever requests it.Often it has an extra number or letter on it to signify that the child has been adopted.
As you say in 1959 the courts would be involved in the adoption.especially as this was a hospital birth to an underage girl.
Once adopted the new parents do not re register the birth but are granted a new short birth certificate via the adoption agency through the courts with new name and original birthdate and birthplace ,this does not have any information about the birth family, this new certificate is not listed on GRO records but on an adoption record that is very difficult to gain access to (unless you are making a TV programme,lol)
Alberta