Hello all, first-time caller and all that

I've recently got back into researching my family history after a long "break", which was partly necessitated by coming up against a brick wall on my father's side of the family. It concerns the identity of my 8th great-grandparent (which is to say I know the names of the other seven).
The problems here are many, at least to my beginner's mind:
My name is Jones, as is my father's, but he took his mother's name, as he seems to have been, in that charming Olde Worlde phrase, born on the wrong side of the blanket, just before the First World War.
I know my great-grandmother's name (Winifred Jones), my grandfather (Maxwell Jones)'s birthdate and birthplace (47 Walton Breck Road, Liverpool, 27/1/1913), but details such as father's name, mother's DOB and other such basic info seems to have been left off my grandfather's birth certificate. My grandfather never talked much about his parents, but the oral history, such as it is, is that his mother, Winifred, was a "servant in a big house in Wiltshire" (possibly Worton) and after falling pregnant (by the master of the house?) went up to Liverpool to have the baby...she then returned to Wiltshire and married Lot Ellis, and together they gave my grandad a half-brother, Edward, who I believe went on to be a big noise in the Navy or something along those lines. Thus I imagine the Ellis line is fairly easy traceable, whereas my own male lineage (my father's father's father's etc. etc. father), at least for me, remains a tricky puzzle to unravel...
Right, that's about it! Would be grateful for any tips on where to go next...Winifred's employment records? The address in Liverpool? etc. The maddening thing is that I can't even pin Winifred down with any certainty in any census, as I have no birthdate...
Advice please!