Thanks for your patient response, Eddie. I should have waited before posting, until I had confirmation of my information, instead of depending on my memory of family conversations. My excitement at finding this forum got the better of my common sense. It's unlikely we have a connection, but I now have some actual facts, so . . . . . . just to get the record straight:
My grandmother was named Elizabeth Catherine (aka Kathleen) Sefton, born Nov 11, 1883 (but remotely possible it was 1884 or 1885), and I've presumed she was born in Liverpool, but don't actually know this for sure. She was raised by another family, probably Wells, which may indicate her mother died when she was quite young. Her mother's maiden name was probably Woods. Her father was William Sefton, mariner, possibly born in the 1850s, probably in Liverpool. Elizabeth Catherine spent some time in service in Ireland, starting about 1898 when she was fourteen, and I will eventually have access to a photocopy of a reference letter from her employers there which should give me more accurate dates. She later married Robert Walter Beams (whose father was also a mariner--a rigger), at St Pauls church in Kirkdale, Liverpool, on April 4th 1904. I've been toldshe may have had sisters in Australia.
I have found no-one in the 1881 or 1901 censuses, the FreeBMD database, the LDS, or any other searchable place on the web, that I can identify as my grandmother Elizabeth Catherine, or her father William. I expect my next step is to get a copy of her marriage certificate--since that is the only exact date and place I have--and do some real research.