The mass-scale integration of electric vehicles into the power system is a key pillar of the European energy transition agenda. Yet, the extent to which such integration would represent a burden for the power system of each member country is still an unanswered question. This is mainly due to a lack of accurate and context-specific representations of aggregate mobility and charging patterns for large electric vehicle fleets. Here, we develop and validate against empirical data an open-source model that simulates such patterns at high (1-min) temporal resolution, based on easy-to-gather, openly accessible data. We hence apply the model – which we name RAMP-mobility – to 28 European countries, showing for the first time the existence of marked differences in mobility and charging patterns across those, due to a combination of weather and socio-economic factors. We hence quantify the impact that fully-electric car fleets would have on the demand to be met by each country's power system: an uncontrolled deployment of electric vehicles would increase peak demand in the range 35–51%, whilst a plausible share of adoption of smart charging strategies could limit the increase to 30–41%. On the contrary, plausible technology (battery density) and infrastructure (charging power) developments would not provide substantial benefits. Efforts for electric vehicles integration should hence primarily focus on mechanisms to support smart vehicle-to-grid interaction. The approach is applicable generally beyond Europe and can provide policy makers with quantitatively reliable insights about electric vehicles impact on the power system.