Deep sequencing of B cell receptor (BCR) heavy chains from a cohort of 31 COVID-19 patients from the UK reveals a stereotypical naive immune response to SARS-CoV-2 which is consistent across patients. Clonal expansion of the B cell population is also observed and may be the result of memory bystander effects. There was a strong convergent sequence signature across patients, and we identified 1,254 clonotypes convergent between at least four of the COVID-19 patients, but not present in healthy controls or individuals following seasonal influenza vaccination. A subset of the convergent clonotypes were homologous to known SARS and SARS-CoV-2 spike protein neutralizing antibodies. Convergence was also demonstrated across wide geographies by comparison of data sets between patients from UK, USA, and China, further validating the disease association and consistency of the stereotypical immune response even at the sequence level. These convergent clonotypes provide a resource to identify potential therapeutic and prophylactic antibodies and demonstrate the potential of BCR profiling as a tool to help understand patient responses.