If you have found the entry in the Birth registers then it is possible to buy the orginial birth certificate.
A family rumour was that a relative gave up baby for adoption after the war, I looked through the birth registers on Ancestry and found an entry which looked likely. On a hunch, I ordered it and it turned out to be the correct one! (A fairly unusual surname and the place of birth aided my search)
As already stated, in the last column is written the word 'Adopted' on the birth certificate.
So yes, providing you have the entry from the birth registers, it is possible to buy the certificate, but there is no link between the birth cert and the adoption cert. Only the adoptee can find that out. So unless you are the adoptee you can find one certificate but not the other!
acceber