A quantitative understanding of people’s mobility patterns is crucial for many applications. However, it is difficult to accurately estimate mobility, in particular during disruption such as the onset of the COVID-19 pandemic. Here, we investigate the use of multiple sources of data from mobile phones, road traffic sensors, and companies such as Google and Facebook in modelling mobility patterns, with the aim of estimating mobility flows in Finland in early 2020, before and during the disruption induced by the pandemic. We find that the highest accuracy is provided by a model that combines a past baseline from mobile phone data with up-to-date road traffic data, followed by the radiation and gravity models similarly augmented with traffic data. Our results highlight the usefulness of publicly available road traffic data in mobility modelling and, in general, pave the way for a data fusion approach to estimating mobility flows.