This paper uses a stochastic simulation methodology to generate a schedule of daily travel and charging profiles for a population of electric vehicles with GPS travel data collected during an electric vehicle demonstration trial. The dependence structure between six variables is modelled using a non-parametric copula function. Then an iterative method of conditional distributions with a Bayesian inference is used to generate travel patterns that comply with the uncertainty of the inputs. At each destination a probabilistic charging model is used to translate the travel patterns of the electric vehicles (EVs) into the respective power demand of the vehicles. These synthetic datasets capture the degree of uncertainty of the travel and charging behaviour of EVs (contrary to single realisations) and are scalable to different EV populations (allowing uncertainty reduction effects in large populations). Such charging profiles would be useful to electric vehicle grid integration studies such as aggregated power demand, power systems services and charging optimisation analyses.