Have you found a death record for the husband? That will help to pin down a timescale when children could have been born. Depending how common the name is, you can try searching "all types" of records on Free BMD
http://www.freebmd.org.uk/cgi/search.pl for the district where they were married or where the known chiild was born for the period 1871-1881. (Obviously this works better for less common surnames - for Smith in Birmingham, it probably won't be an option!)
You might be able to find the family in a contemporary street directory, although this will only list the householder, not other family members.
Otherwise, local parish records are a possibility.
Have you found the mother and child in 1891? Occasionally part of the family was away from home on census night, and you find everyone back together again on the following census.
Post names and dates, and I'm sure someone will come up with more ideas!
Rambler
