Mandatory annual reporting, to improve transparency of working conditions in firms' supply chains, is the favored approach of UK policymakers for reducing modern slavery risks in supply chains. Despite legislation and extensive guidance, annual corporate statements are disappointing, providing little evidence of substantive action. So far though, there has been little primary research of managers' understanding of the phenomenon or their perceived agency in tackling modern slavery. In a qualitative study, employing template analysis, data were drawn from multiple sources, including interviews with 32 managers from three large UK firms in a complex, high‐risk sector (construction). Four focus groups were used to establish credibility of the findings. As managers struggle with how to make sense of where to look, how to look, and what to see, they adopt narrowed perspectives and analogies that inhibit immediate, compelling action. Improved awareness of UK labor supply chain issues has distanced managers further from action relating to global material supply chains. Through analogy with health and safety legislation, which developed over a considerable period, managers justify a wait‐and‐see approach, deferring action. Such convenience framing helps them to avoid issues relating to complexity, control, cost, and (in)visibility. This framing needs to be disrupted for meaningful action to result. Drawing on sensemaking theory relating to paradoxical financial and sustainability objectives, the study suggests how extended legislation and governance may drive more substantive responses that transcend the constraints of business‐case logic.