Yes I have a 1852 birth in Essex that is not registered and I have tried all names under the sun and no luck. I also think it was common in County Durham as well as Liverpool, London and Surrey, where it is reported the highest number of unregistered births took place.
Until 1875 it was the duty of the registrar and his deputies to scour the registration district taking notes of any new births. Must have worked with local midwives or if the birth was not with a midwife, they got info from local shops, pubs etc. From 1875 the parents (or at least one of them) had to trot off to the registry office and register the birth themselves.