You may wish to take a look at the following which is a section from the from this document.
http://www.ips.gov.uk/cps/files/ips..._Full_Birth_Certificate_Policy_TO_PUBLISH.pdf
Re-registration of births
In some circumstances a child’s name can be changed by re-registering the birth. No other evidence of change of name is needed in such cases.
The General Register Office (GRO) has confirmed that there are no time limits for re-registration of births and upon re-registration the name can be changed. Re-registration can usually take place under one of the following criteria:
• To include natural father’s details
• Where the natural parents subsequently marry each other
England, Wales and Northern Ireland
Where the parents have not married each other and the mother initially registers the birth without any father’s particulars, both parents can then apply to re-register the birth to include his details at a later date. This would take place under section 10a of the Births and Deaths Registration Act 1953. A change of surname for the child in the new registration is possible if both parents agree. If the child is aged 16 or over, the child’s agreement is also necessary. GRO would also make further enquiries to ascertain whether any court order is in existence to prohibit a change of surname.
If the parents are not married to each other, the birth may initially be registered either by the mother alone or on the joint information of both parents. Upon their marriage the parents should apply to re-register the birth to show the child as a child of their marriage. This would take place under section 14 of the Births and Deaths Registration Act 1953. Re-registration of a birth upon the parents' marriage has been possible in England and Wales since 1927. GRO would also make further enquiries to ascertain whether any court order preventing any change to the child’s surname, otherwise the conditions are as set out in the above paragraph. Examiners should be aware that it is the subsequent marriage of the parents that legitimates the birth and not the re-registration itself.
The legal advisors team for GRO have stated that the child’s surname may only be changed to:
1) The father’s surname
2) The mother’s surname
3) A combination of the two
4) The mother’s maiden surname or,
A relevant surname where the parents follow a different cultural custom
On occasions a re-registration will be offered when the incorrect father has been initially registered as father. If it is then proven to the Registrar General’s satisfaction that that man is not the natural father, a correction is then made to the birth entry to effectively remove his details. Following this, the way is then clear for the mother and the natural father to apply to re-register the birth to include his details as father.
In all cases when a re-registration has been effected the words “On the authority of the Registrar General” are displayed after the date of registration on the full birth certificate.