From
http://www.ukdps.co.uk/
CanABirthCertificateBeChanged.html:
Changing a child's surname from the mother's surname to the father's surname (parents not married):
If the natural parents of the child were not married to each other at the time of the birth and the father did not attend with the mother to register the child, it is possible to re-register the birth at any time in the future to include the father's details and change the surname of the child to that of the father (only if both parents agree, otherwise a court order is required). Upon re-registration, a new birth certificate can be purchased.
You may want to visit a hospital and talk with someone there to confirm the name issue.