In agreement with @MikeVaughan, I'm going to say that using the plural conjugation is incorrect, and the sentence would need to be reformulated. The verb is referring to a single unit, which just happens to be a collection of things. If you want to save the second part of that phrase, I'd change the verb to shift focus from the container to its contents, for instance
[...]One such family contains the genes for human haemoglobin subunits;[...]
[...]One such family consists of the genes for human haemoglobin subunits;[...]
EDIT: To cover my comment on @Jimi Oke's answer, I'd argue that "genes" is very much the subject complement of this sentence, by its definition as the noun following the subject and linking verb, and as such, the linking verb and the complement should both agree with their preceding noun in quantity. An example of this would be:
[...]One such family is the group of genes for human haemoglobin subunits;[...]
Indeed, the OP could avoid the problem altogether by saying
[...]One such family of genes [describes, dictates, your-choice-here] human haemoglobin subunits.
I can't think of a way to simply remove "family" (or any equivalent word) as the subject of the sentence and make "genes" the subject without destroying the meaning.