Knowing the surname (and maiden name of the mother if she was married at the time), can help to find the correct birth record. The birth certificate can then be obtained either from the GRO or Lincolnshire Registration Services (the latter option does not require a GRO reference number). The right hand column of the certificate will note an adoption took place but not any change of name resulting from it.
I was born in Lincoln in '66 and adopted, my search started back in 2005 (pre DNA), & I managed to piece quite a bit together from the birth index though documents can have some missing or questionable information on them so DNA is always a good idea but unless your sibling or their descendant has tested there may not be a close match in the results.