This is exactly the kind of situation I was thinking of. I had long suspected that the father on my wife's great grandmother's marriage certificate was bogus as it states simply 'Father - Frederick Jackson - clerk' i.e. telling us almost nothing about him and there is no other record of such a person ever existing. I think I now have the right birth certificate but that gives the father as 'George Stuart Jackson - Journeyman tailor' i.e. a good deal more plausible detail but once again there is no other record of this individual . As the mother is described as Jackson formerly Jackson, this is quite likely an incestuous birth, the lack of any corroborating evidence being possibly explained by the fact that the lady in question was Irish and may only recently have arrived in England. She appears in the 1871 census running a boarding house in London, a description which could cover a multitude of sins... She then disappears never to be heard of again.
What really put me onto the possibility of a widespread issue under such circumstances was while conducting research into the illegitimate children of James Disraeli, brother of the Victorian prime minister, Benjamin. We know that his mistress, Mary Bassett had had one illegitimate child (William) before the relationship with James, the birth certificate simply giving no details of the father but when he marries some 25 years later, his father is stated to be 'William Bassett - deceased' which really does look suspect.
I could quote several other cases in our immediate families too, added to which I have never seen a marriage certificate with a blank in the father's name field although from what we know of Victorian England, this ought to have been commonplace. Perhaps the authorities were actually turning a well-meaning blind-eye to the practice?