Burnout amongst healthcare professionals has been a long-considered condition associated with the workplace environment. Student nurses studying at Sheffield Hallam University continued to engage in their training during the COVID-19 pandemic; however, the stressors of this experience were anecdotally highlighted to their academic staff. Furthermore, burnout can be linked to the ongoing difficulties with recruitment and retention of nursing staff within the NHS workforce. This work aimed to determine the burnout among nursing students experience by obtaining quantitative data to understand their experiences. The Copenhagen Burnout Inventory was used to gauge levels of burnout across the different fields of nursing students. Results identified that: (1) mental health students reported feeling tired significantly less often than child and adult field students (mean rating of 69% versus 91.7% and 84.0%, respectively); (2) students aged 30–39 feel tired significantly less often than both younger student age groups (mean rating 59.4% versus 82.8% and 90.6%); (3) there was a significant difference in how often different age groups felt “tired of working with clients” (F(4) = 2.68, p = 0.04) and that “they couldn’t take it anymore” (F(4) = 2.53, p = 0.05); (4) child-field students reported generally higher levels of global burnout (mean CBI total = 57.9%) whilst mental health students reported lower levels (mean CBI total = 54.1%). Considering these results, it is imperative for both higher education institutions and potential employers to consider the impact of COVID-19 and burnout, and the levels of support offered to student nurses during their training and transition to practice as newly qualified nurses.