Despite considerable work applying ab initio techniques to model the role of defects on mechanical, structural and electronic properties of oxides, there has been little on the role of trapped hydrogen, despite it being virtually always present. We propose a framework for identifying reversible and irreversible hydrogen traps. We demonstrate that the thermodynamic stability of oxy-hydroxyl defects is defined by an interplay of formation and binding energies. This framework is applicable to all oxides and is essential for describing the solubility and diffusivity of hydrogen at the macroscopic level. For the most important actinide oxide in nuclear energy, uranium oxide, hydrogen significantly impacts the stability of oxygen defect clusters, and with increased local hydrogen concentration it forms irreversible traps. Crucially, hydrogen stabilises isolated Willis clusters, named after their discoverer and originally reported in 1963, which all subsequent ab initio calculations have predicted to be unstable, but of course, none considered hydrogen.