I'm assuming that this is Thomas's birth - MMN blank, implying she was unmarried.
FITZPATRICK, THOMAS -
GRO Reference: 1877 M Quarter in PRESCOT Volume 08B Page 699
Therefore Margaret (assuming she was the mother) could have married any time from Q1 1877 - Q1 1881 and would show on the census under her married name, assuming she remained in the UK.
Using Lancashire BMD & cross-referencing the 1881 ones with FreeBMD, there are 10 potential marriages in this period.
Many illegitimate children were left with grandparents or other family members, including my own Great Grandfather. It wasn't at all unusual.