Many countries have banned groups and gatherings as part of their response to the pandemic caused by the coronavirus, SARS-CoV-2. Although there are outbreak reports involving mass gatherings, the contribution to overall transmission is unknown. We used data from a survey of social contact behaviour that specifically asked about contact with groups to estimate the population attributable fraction (PAF) due to groups as the relative change in the basic reproduction number when groups are prevented. Groups of 50+ individuals accounted for 0.5% of reported contact events, and we estimate that the PAF due to groups of 50+ people is 5.4% (95% confidence interval 1.4%, 11.5%). The PAF due to groups of 20+ people is 18.9% (12.7%, 25.7%) and the PAF due to groups of 10+ is 25.2% (19.4%, 31.4%). Under normal circumstances with pre-COVID-19 contact patterns, large groups of individuals have a relatively small epidemiological impact; small- and medium-sized groups between 10 and 50 people have a larger impact on an epidemic. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.