There is a well-recognised mental health and wellbeing crisis among the undergraduate population in UK higher education. However, the wellbeing of postgraduate research students (PGRs) and the effectiveness of university strategies in supporting PGR wellbeing are much less understood. Early research shows that PGRs' wellbeing is impacted by their loneliness. These initial studies are limited; however, primarily considering loneliness using qualitative approaches and treating it as a unidimensional phenomenon. Our study addresses these limitations, using a quantitative approach to investigate the impact of loneliness (as a multidimensional phenomenon) on PGR wellbeing and the effectiveness of institutional strategies to support PGR wellbeing. We conduct regression analyses on the wellbeing of PGRs, focusing on components of loneliness and stress as predictors. Analysis demonstrates that social loneliness and stress separately predict lower PGR wellbeing. Further analysis reveals that PGRs who experience both social loneliness and stress have additional declines in their wellbeing. Results also suggest that typical strategies used by universities to support students are ineffective within the PGR community. Findings improve understanding of the nature of PGR wellbeing and loneliness, providing a platform for further work to improve PGR support and wellbeing.