While I can understand that your son would like to see his name on the birth certificate, I think that his main objective would seem to be to acquire parental responsibility.
Your son will automatically acquire parental responsibility if he acts
with the child's mother to have his name added to the birth certificate. This presents obvious difficulties. However, this is not the only way in which he can acquire parental responsibility. He can also seek a court order. He might need a solicitor to help with this but, in the first instance, he can seek advice from ParentLine Plus on 0808 800 2222.
This post is based upon information from these two pages of the General Register Office website:
http://www.gro.gov.uk/gro/content/births/canic hangethebirthrecordatalaterdate/birth3e.asp
and
http://www.gro.gov.uk/gro/content/births/paren talresponsibility/index.asp
Chris