Probably, as suggested by GDoS, from the following sense of crib:
(SE crib, a container for animal fodder)
(Aus./N.Z.) a snack, a light meal, a piece of bread, cake etc; thus crib bag, crib break, crib room, cribtime.
1870 [UK] Old Hunks in Darkey Drama 5 53: harry: I’m witness that you promised to give Tommy something better than a crib. tommy: A good round dinner.
1900–10 [Aus] Stephens & O’Brien Materials for a Dict. of Aus. Sl. [unpub. ms.] 52: CRIB: miners term for a twenty-minute interval for food or smoke-ho, known as crib-time; and lunch carried to work is known as crib.
The Cornish origin seems plausible. From List of Cornish dialect words:
Crib - a mid-morning break for a snack.
The Oxford English Dictionary (2nd ed.) has "Food, provisions, light meal, etc." (dialectal) as one of the meanings of "crib" giving several examples including quotations from M. A. Courtney's Glossary (1880) and Rowse's Cornish Childhood (1942).