Avian influenza is a global public health threat. Since 2021, the ongoing H5N1 panzootic has brought a major shift in H5Nx epidemiology, including unprecedented spread, wide host range and lack of seasonality. Infections in marine mammals, wildlife and livestock have heightened concern for human-to-human transmission and pandemic potential. Contact tracing and self-isolation are used as public health measures in the UK to manage contacts of confirmed human cases of avian influenza. In this study, we aimed to estimate potential outbreak sizes and evaluate the effectiveness of contact tracing and self-isolation in managing community outbreaks of H5N1 following spillover from birds to people. We characterised contact patterns from an underrepresented agricultural population at high risk of avian influenza exposure through contact with birds (Avian Contact Study). Informed by these realistic social contact data, we modelled outbreak sizes using a stochastic branching process model. Most simulations resulted in small-scale outbreaks, ranging from 0 to 10 cases. When the basic reproduction number was 1.1, contact tracing and self-isolation reduced the average outbreak size from 41 cases (95% Confidence Interval (CI): 37-46 cases) to 7 cases (95% CI: 6-8 cases), preventing, on average, 8 out of every 10 infections. However, controls became less effective in reducing the outbreak size when a higher proportion of cases were asymptomatic. Overall, our findings suggest that contact tracing and self-isolation can be effective at preventing zoonotic infections. Increasing awareness, encouraging self-isolation, and detecting asymptomatic cases through routine surveillance are important components of zoonotic infection containment strategies.