A line and method for the production of covered cardboard boxes are disclosed. The line includes a conveyor unit including a belt and a conveyor actuator that drives the belt intermittently in an alternating sequence of movements and stops. A feed unit individually feeds covering blanks from a reservoir to the conveyor unit in a sequence of feed instants. An erecting machine folds box blanks into corresponding boxes. A positioner individually positions the boxes from the erecting machine, in alignment on corresponding covering blanks disposed on the belt of the conveyor unit. A gluer spreads glue on one face of the covering blanks. A covering machine folds the covering blanks into contact with their respective boxes to cover the boxes. A control unit connected to the feed unit adjustably sets a phase displacement of the feed instants relative to the sequence of stops of the belt.