A novel SARS-CoV-2 variant, VOC 202012/01, emerged in southeast England in November 2020 and is rapidly spreading towards fixation. Using a variety of statistical and dynamic modelling approaches, we assessed the relative transmissibility of this novel variant. Depending on the analysis, we estimate that VOC 202012/01 is 43–82% (range of 95% credible intervals 38–106%) more transmissible than preexisting variants of SARS-CoV-2. We did not find clear evidence that VOC 202012/01 results in greater or lesser severity of disease than preexisting variants. Nevertheless, the increase in transmissibility is likely to lead to a large increase in incidence. To assess the potential impact of VOC 202012/01, we fitted a two-strain mathematical model of SARS-CoV-2 transmission to observed COVID-19 hospital admissions, hospital and ICU bed occupancy, and deaths; SARS-CoV-2 PCR prevalence and seroprevalence; and the relative frequency of VOC 202012/01. We find that without stringent control measures, COVID-19 hospitalisations and deaths are projected to reach higher levels in 2021 than were observed in 2020. Control measures of a similar stringency to the national lockdown implemented in England in November 2020 are unlikely to reduce the effective reproduction number Rt to less than 1, unless primary schools, secondary schools, and universities are also closed. We project that large resurgences of the virus are likely to occur following easing of control measures. It may be necessary to greatly accelerate vaccine roll-out to have an appreciable impact in suppressing the resulting disease burden.