Transmission of SARS-CoV-2 is uncontrolled in many parts of the world; control is compounded in some areas by the higher transmission potential of the B.1.1.7 variant1, which has now been reported in 94 countries. It is unclear whether the response of the virus to vaccines against SARS-CoV-2 on the basis of the prototypic strain will be affected by the mutations found in B.1.1.7. Here we assess the immune responses of individuals after vaccination with the mRNA-based vaccine BNT162b22. We measured neutralizing antibody responses after the first and second immunizations using pseudoviruses that expressed the wild-type spike protein or a mutated spike protein that contained the eight amino acid changes found in the B.1.1.7 variant. The sera from individuals who received the vaccine exhibited a broad range of neutralizing titres against the wild-type pseudoviruses that were modestly reduced against the B.1.1.7 variant. This reduction was also evident in sera from some patients who had recovered from COVID-19. Decreased neutralization of the B.1.1.7 variant was also observed for monoclonal antibodies that target the N-terminal domain (9 out of 10) and the receptor-binding motif (5 out of 31), but not for monoclonal antibodies that recognize the receptor-binding domain that bind outside the receptor-binding motif. Introduction of the mutation that encodes the E484K substitution in the B.1.1.7 background to reflect a newly emerged variant of concern (VOC 202102/02) led to a more-substantial loss of neutralizing activity by vaccine-elicited antibodies and monoclonal antibodies (19 out of 31) compared with the loss of neutralizing activity conferred by the mutations in B.1.1.7 alone. The emergence of the E484K substitution in a B.1.1.7 background represents a threat to the efficacy of the BNT162b2 vaccine.