I'm donor conceived, but my dad (as in the man who brought me up) is named as my father on my birth certificate. Don't know if legislation is any different now, but it's not made a difference that it isn't biologically accurate
If your parents were married there was always an automatic assumption the man your mother was married to goes on the bc. That still applies- the husband of a married surrogate is still the default father.
If your parents weren't, your mother's partner could simply have gone along with your mother to register the birth - same as any unmarried father.
There are other permutations, including 2 mothers , one of whom will have no genetic connection to the child.
www.gov.uk/register-birth/who-can-register-a-birth