Following the Brexit referendum, the United Kingdom's Department for Food, Environment and Rural Affairs (Defra) began to "co-design" a new agri-environment policy for England with stakeholders: the environmental land management (ELM) scheme. ELM is the cornerstone of the most far-reaching agricultural policy reforms undertaken in the UK since the Second World War. This article provides the first empirically grounded assessment of the ELM co-design process. It uses a framework developed by science and technology studies (STS) scholars to help remake participation along constructivist lines to show where, how and why the co-design process was constrained by sociotechnical systems and constitutional relations between citizens, science and the state. Our analysis shows that while STS-informed interventions can help make government-orchestrated participation more experimental, reflexive, anticipatory and responsible, remaking it along constructivist lines requires a new constitutional moment in which major changes are made to the arrangement of epistemic and political authority. With the popularity of co-design rising with governments across the world, our article is relevant to a broad international readership wanting to know more about how co-design fares in the context of large-scale systemic transformations.