The European automotive industry is a major consumer of materials, contributing significantly to resource depletion and environmental pressures from raw material extraction and processing. With growing demand for mobility and the rising material intensity of electric vehicles, driven largely by batteries and their critical raw materials, transitioning to a circular economy is essential to reduce the sector's environmental impact. In this paper we quantify the circularity potential of the EU27 automotive industry using a system-dynamic model of light private vehicles from 2000 to 2050. We simulate circular measures involving both technological improvements (e.g., material efficiency and recycling) and behavioral changes (e.g., car occupancy and modal shifts). We show that, under a business-as-usual scenario, the material demand of the European automotive sector would rise by around 50% by 2050. While circular measures by manufacturers and recyclers can slow this trend, only when combined with behavioral changes can they significantly curb material demand and partially close the loop. We estimate that these combined measures could save around 350 million tonnes of materials by 2050, with the most substantial gains resulting from reduced travel distances, shifts to public transport, and increased ridesharing. The circularity rate – defined as the ratio between material recovery and demand – could increase from 27% today to 80% by 2050. Our findings highlight the need to integrate demand-side measures with supply-side innovations to reduce material consumption and achieve high circularity in the automotive sector.