Electric vehicles (EVs) integration in modern power systems has modified the nature of traditional power demand, which brings uncertainties in the energy consumption end. Such uncertainties may lead to a variety of influences on the performance of EV applications in power systems. This paper focuses on the EV application to load levelling in the UK. Six EV uncertainties are specified to analyze the impact on three parameters, which describe the performance of load levelling. The UK EV and power system data are used in the case study. The simulation results show that the battery sizes, discrete accuracy, and driving behavior have little influence on the load levelling results; a better load levelling result can be obtained with larger EV scales, larger discharging available capacity, and longer available time duration; inappropriate selection of available time duration may worsen the ramps, which bring challenges to conventional generators.