For whatever reason (possibly due to moving house), the family clearly eluded the enumerator in 1871 and are not recorded.
Unless, for some unknown reason, they changed their surname. Ancestors of my husband did exactly that on one of the census, using the wife's mother's maiden name.

I wonder why they didn't want to be found? By the following census they were back with their real names.
Anyway, the way I found them was by searching on Ancestry using just their first names. So LockerZ could try that.