The Observatory for Monitoring Data-Driven Approaches to Covid-19 (OMDDAC) is an Arts and Humanities Research Council funded research project investigating data-driven approaches to Covid-19, focused upon legal, ethical, policy and operational challenges. The project is a collaboration between Northumbria University (Law School, Department of Computing and Information Sciences, Department of Mathematics) and the Royal United Services Institute, a defence and security think-tank, and aims to carry out integrated interdisciplinary research, regarded as the most challenging type of interdisciplinarity but where the outputs can be the most impactful. Due to the constraints of the pandemic, the project has been carried out in a fully distributed and remote manner, with some team members never having met in person. The subject of the research is continually changing and developing, creating unique project management issues, with the impact of the pandemic pervasive in the lives of the researchers. This article takes the form of a series of reflections from the points of view of individual project researchers – the specialist legal researcher, the think-tank Co-Investigator, the post-doctoral researcher, statistical and data science researchers, and the Principal Investigator – and organised under two main themes - project management and internal communication; and methodologies/interdisciplinary research. We thus draw out lessons for future remote and distributed research, focused upon interdisciplinarity, the benefits and challenges of remote research methodologies, and issues of collegiality. Finally, we warn that it will be a false economy for universities and funders to assume that research projects can continue to be conducted in a mainly remote manner and therefore, that budgetary savings can be made by reducing time allocations, travel and academic networking.