Sue, you may not realize that what applies in England does not apply everywhere.
In the US (unless something has changed very recently that I don't know about), people do not have access to their original birth certificates, and they are not given parent information. The records are simply sealed. In Ontario, Canada, where I live, it was only a very few years ago that new rules were made to give adoptees that access, and the rules are not retroactive.
In any case, a birth certificate anywhere might not identify the father, and you can't do your father's side of your family tree if you don't know his name.