Retrospective analyses of the non-pharmaceutical interventions (NPIs) used to combat the ongoing COVID-19 outbreak have highlighted the potential of optimizing interventions. These optimal interventions allow policymakers to manage NPIs to minimize the epidemiological and human health impacts of both COVID-19 and the intervention itself. Here, we use a susceptible-infectious-recovered (SIR) mathematical model to explore the feasibility of optimizing the duration, magnitude and trigger point of five different NPI scenarios to minimize the peak prevalence or the attack rate of a simulated UK COVID-19 outbreak. An optimal parameter space to minimize the peak prevalence or the attack rate was identified for each intervention scenario, with each scenario differing with regard to how reductions to transmission were modelled. However, we show that these optimal interventions are fragile, sensitive to epidemiological uncertainty and prone to implementation error. We highlight the use of robust, but suboptimal interventions as an alternative, with these interventions capable of mitigating the peak prevalence or the attack rate over a broader, more achievable parameter space, but being less efficacious than theoretically optimal interventions. This work provides an illustrative example of the concept of intervention optimization across a range of different NPI strategies. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.