Hi Paul,
Welcome to rootschat

I can see your grandfather in 1901 with wife Lily, but no children (yet?).
Going back from 1881 to
1871, this is the most likely family I can see:
RG10/3759 31 59
Liverpool St Titus, Lancashire
(40?) Mile End Samuel Brailford, head, 26 or 36, Labourer, b. Ireland
Bridget, wife, 24, b. Ireland
Thomas, son, 2, b. Lancashire Liverpool
Samuel, son, 5ms, b. Liverpool
Thomas Devaney (?), boarder, unm, 21, Labourer, b. Liverpool
I'm having a look on later census returns to see if I can find them.
Tanja