Engagement and burnout in university students have serious implications for mental health, well-being and academic success (performance and retention). This study aimed to investigate possible predictors of engagement and burnout in UK university students, drawing on previous research from positive psychology. A sample of UK university students (*N* = 133) completed a questionnaire online or face-to-face, containing measures of strengths use, deficits improvement, hope, efficacy, engagement and burnout. Results showed that engagement was correlated with all variables and predicted by strengths use, deficits improvement and hope, and burnout was correlated with all variables and predicted by hope. The implications of these results are that interventions to increase engagement and decrease burnout should focus on increasing strengths use, deficits improvement, hope and efficacy in university students. This study made an important contribution to existing research as it was the first investigation of strengths use and deficits improvement in UK university students and it validated the SUDCO scale for this population. In addition, this study built on existing research by providing further insight into the role of hope and efficacy in engagement and burnout in university students. Future studies should extend this research by investigating the effectiveness of strengths use, deficits improvement, hope and efficacy interventions for increasing engagement and decreasing burnout. Effective interventions are of paramount importance given the impact of engagement and burnout on university students’ mental health, well-being and academic success. *Keywords*: engagement, burnout, strengths use, deficits improvement, hope, efficacy