Thats how it should work. You start with say a Birth Cert' on this is the child plus the mother and the father [or at least in the majority of cases] from this you find the marriage of the parents. On the marriage cert it shows the bride & groom plus the brides father & the grooms father & as you say you now have a male or female plus their father and so need the B/Cert this when obtained then shows you the mother. So from each cert you gain an additional piece of info [marriage cert gives you the father & then the B/C will show you the mother]. So if you do know the child plus father you can order a search over a defined period from the G.R.O on line or by telephone.