Both natural infection with SARS-CoV-2 and immunization with a number of vaccines induce protective immunity. However, the ability of such immune responses to recognize and therefore protect against emerging variants is a matter of increasing importance. Such variants of concern (VOC) include isolates of lineage B1.1.7, first identified in the UK, and B1.351, first identified in South Africa. Our data confirm that VOC, particularly those with substitutions at residues 484 and 417 escape neutralization by antibodies directed to the ACE2-binding Class 1 and the adjacent Class 2 epitopes but are susceptible to neutralization by the generally less potent antibodies directed to Class 3 and 4 epitopes on the flanks RBD. To address this potential threat, we sampled a SARS-CoV-2 uninfected UK cohort recently vaccinated with BNT162b2 (Pfizer-BioNTech, two doses delivered 18-28 days apart), alongside a cohort naturally infected in the first wave of the epidemic in Spring 2020. We tested antibody and T cell responses against a reference isolate (VIC001) representing the original circulating lineage B and the impact of sequence variation in these two VOCs. We identified a reduction in antibody neutralization against the VOCs which was most evident in the B1.351 variant. However, the majority of the T cell response was directed against epitopes conserved across all three strains. The reduction in antibody neutralization was less marked in post-boost vaccine-induced than in naturally-induced immune responses and could be largely explained by the potency of the homotypic antibody response. However, after a single vaccination, which induced only modestly neutralizing homotypic antibody titres, neutralization against the VOCs was completely abrogated in the majority of vaccinees. These data indicate that VOCs may evade protective neutralising responses induced by prior infection, and to a lesser extent by immunization, particularly after a single vaccine, but the impact of the VOCs on T cell responses appears less marked. The results emphasize the need to generate high potency immune responses through vaccination in order to provide protection against these and other emergent variants. We observed that two doses of vaccine also induced a significant increase in binding antibodies to spike of both SARS-CoV-1 & MERS, in addition to the four common coronaviruses currently circulating in the UK. The impact of antigenic imprinting on the potency of humoral and cellular heterotypic protection generated by the next generation of variant-directed vaccines remains to be determined.