BACKGROUND: In line with movement restrictions and physical distancing essential for the control of the COVID-19 pandemic, WHO recommended postponement of all neglected tropical disease (NTD) control activities that involve community-based surveys, active case finding, and mass drug administration in April, 2020. Following revised guidance later in 2020, and after interruptions to NTD programmes of varying lengths, NTD programmes gradually restarted in the context of an ongoing pandemic. However, ongoing challenges and service gaps have been reported. This study aimed to evaluate the potential effect of the programmatic interruptions and strategies to mitigate this effect. METHODS: For seven NTDs, namely soil-transmitted helminths, schistosomiasis, lymphatic filariasis, onchocerciasis, trachoma, visceral leishmaniasis, and human African trypanosomiasis, we used mathematical transmission models to simulate the effect of programme interruptions on the dynamics of each of these diseases in different endemic settings. We also explored the potential benefit of implementing mitigation strategies, primarily in terms of minimising the delays to control targets. FINDINGS: We show that the effect of the COVID-19-induced interruption in terms of delay to achieving elimination goals might in some cases be much longer than the duration of the interruption. For schistosomiasis, onchocerciasis, trachoma, and visceral leishmaniasis, a mean delay of 2-3 years for a 1-year interruption is predicted in areas of highest prevalence. We also show that these delays can largely be mitigated by measures such as additional mass drug administration or enhanced case-finding. INTERPRETATION: The COVID-19 pandemic has brought infectious disease control to the forefront of global consciousness. It is essential that the NTDs, so long neglected in terms of research and financial support, are not overlooked, and remain a priority in health service planning and funding. FUNDING: Bill & Melinda Gates Foundation, Medical Research Council, and the UK Foreign, Commonwealth & Development Office.