Understanding the composition of human immune responses to SARS-CoV-2 and vaccines is essential for predicting protection from infection and determining vaccine efficacy. Here, we explored T-cell immune responses to SARS-CoV-2 and the UK (B.1.1.7) variant of concern (VOC) in infected and vaccinated individuals. In infected patients, CD4+ T-cells demonstrated consistent, robust responses against Spike peptides, while CD8+ T-cells had heterogeneous responses to 5 SARS-CoV-2 proteins. We found 80% of infected and vaccinated individuals showed positive CD4+ T-cell immunity against SARS-CoV-2. Moreover, CD4+/CD8+ T-cell responses to SARS-CoV-2 and the United Kingdom (B.1.1.7) variant are robust and nearly identical in infected and vaccinated individuals. Thus, the UK variant did not interfere with T-cell recognition and elicited responses. These observations will be of critical importance in assessing human immune responses to emerging VOCs.