Recent findings suggest that an adequate test-trace-isolate (TTI) strategy is needed to prevent a secondary COVID-19 wave with the reopening of society in the UK. Here we assess the potential importance of mandatory masks in the parts of community and in secondary schools. We show that, assuming current TTI levels, adoption of masks in secondary schools in addition to community settings can reduce the size of a second wave, but will not prevent it; more testing of symptomatic people, tracing and isolating of their contacts is also needed. To avoid a second wave, with masks mandatory in secondary schools and in certain community settings, under current tracing levels, 68% or 46% of those with symptomatic infection would need to be tested if masks' effective coverage were 15% or 30% respectively, compared to 76% and 57% if masks are mandated in community settings but not secondary schools.