Effective communication is essential for delivering public health messages and enabling behaviour change. Little is known about possible backfiring, or spillover effects, of COVID-19 vaccine messaging. In a study with n = 1,848 United Kingdom (UK) adults, we assess whether communication strategies that target vaccine hesitancy have any unintended, positive or negative, spillover effects on people's intention to engage in protective, compliance and prosocial behaviours. In June–July 2021, we conducted an online experiment to assess the potential spillover effects of three messages, emphasising (a) the medical benefits of COVID-19 vaccination, (b) the non-medical collective benefits of vaccination or (c) the non-medical individual benefits of holding a vaccination certificate. Exposure to different messages did not significantly affect people's intention to engage in protective, compliance, or prosocial behaviours. Instead, vaccination status (being vaccinated vs not) was positively associated with intentions to engage in protective, compliance and prosocial behaviours. Our results suggest that communication strategies that aim to increase vaccination uptake do not have any unintended effects on other health behaviours and vaccination campaigns can be tailored to specific populations to increase uptake and compliance.