High-income countries (HICs) which are said to have "reached" universal health coverage (UHC) typically still have coverage gaps, due to both formal policies and informal barriers which result in "hypothetical access". In England, a user fee exemption has in principle made access to treatment for post-traumatic stress disorder (PTSD) and other mental health conditions thought to be caused by certain forms of violence universal, regardless of immigration status. This study explores the everyday governance of this mental health coverage for forced migrants in the English National Health Service (NHS) and NGO sector. Fieldwork was conducted in two waves, in 2015-2016 and 2019-2021, including six months of participant observation in an NGO and 21 semi-structured interviews with psy professionals across 16 NHS and NGO service providers. Further interviews were conducted with mental health commissioners and policymakers, as well as analysis of grey literature. Despite being formally covered for certain types of mental health care, in practice asylum seekers and undocumented migrants were often excluded by NHS providers. Undocumented migrants were also often excluded by NGO providers. Several rationalities linked discursive fields to practices developed by psy professionals and other street-level bureaucrats to govern coverage, in a process of "managing failure". These rationalities are presented under three paired themes which draw attention to tensions and resistance in the governance of coverage: medicalisation and biolegitimacy; austerity and ethico-politics; and differential racialisation and decolonisation. Rationalities were associated with strategies and tactics such as social triage, clinical advocacy, obfuscation, evidence-based advocacy and silencing critique. The concept of "health coverage assemblage" is introduced to explain the complex, unstable, contingent and fragmented nature of UHC policies and programmes. Misrecognition and underestimation of the everyday work of health professionals in promoting, resisting and reproducing diverse rationalities within the assemblage may lead to missed opportunities for reform.