The original birth entry ( if you know the birth name and get a copy) will have the same information as any other - but will be marked as "adopted" in the margin.
After the adoption a certificate is issued from the ACR (Adopted Children Register). That will have the same date of birth, but the place of birth may only be shown as a country e.g. England, or later it may give the registration district. If it is a full copy it will also have details of the court authorising the adoption and the names of the adoptive parents.
Adopted children were usually given, or use, the short version of the ACR certificate because that makes no reference to adoption.