While your mother committed a criminal offence by providing incorrect details, your birth certificate remains 'legal' for such purposes as obtaining a passport or otherwise proving your identity.
For obvious reasons, nobody knows exactly how many birth certificates contain incorrect information relating to the child's biological father, but I've heard it suggested (on Radio 4 programmes) that the figure is likely to be at least 10% of all birth certificates, and possibly much higher. Your situation is far from unusual and (from a solely legal perspective) no cause for concern.
There are certain circumstances under which a birth certificate can be altered. They probably don't apply to you but, for completeness, I'll provide the relevant link:
http://www.direct.gov...birthrecord/index.htm
Chris