Green’s Dictionary of Slang

married; thus cut and carry n., a wife.

1935		A.J. Pollock Und. Speaks 28/2: Cut and carry, the wife.
1960		J. Franklyn Dict. of Rhy. Sl.
1971		J. Jones Rhy. Cockney Sl.
2002		M. Coles More Bible in Cockney 99: They ain’t to sleep around and mess around with sex unless they’re cut-and-carried.