The dynamics of immunity are crucial to understanding the long-term patterns of the SARS-CoV-2 pandemic. Several cases of reinfection with SARS-CoV-2 have been documented 48-142 days after the initial infection and immunity to seasonal circulating coronaviruses is estimated to be shorter than 1 year. Using an age-structured, deterministic model, we explore potential immunity dynamics using contact data from the UK population. In the scenario where immunity to SARS-CoV-2 lasts an average of three months for non-hospitalized individuals, a year for hospitalized individuals, and the effective reproduction number after lockdown ends is 1.2 (our worst-case scenario), we find that the secondary peak occurs in winter 2020 with a daily maximum of 387 000 infectious individuals and 125 000 daily new cases; threefold greater than in a scenario with permanent immunity. Our models suggest that longitudinal serological surveys to determine if immunity in the population is waning will be most informative when sampling takes place from the end of the lockdown in June until autumn 2020. After this period, the proportion of the population with antibodies to SARS-CoV-2 is expected to increase due to the secondary wave. Overall, our analysis presents considerations for policy makers on the longer-term dynamics of SARS-CoV-2 in the UK and suggests that strategies designed to achieve herd immunity may lead to repeated waves of infection as immunity to reinfection is not permanent. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.