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Predicting the end-of-life or remaining useful life of batteries in electric vehicles is a critical and challenging problem, predominantly approached in recent years using machine learning to predict the evolution of the state-of-health during repeated cycling. To improve the accuracy of predictive estimates, especially early in the battery lifetime, a number of algorithms have incorporated features that are available from data collected by battery management systems. Unless multiple battery data sets are used for a direct prediction of the end-of-life, which is useful for ball-park estimates, such an approach is infeasible since the features are not known for future cycles. In this paper, we develop a highly-accurate method that can overcome this limitation, by using a modified Gaussian process dynamical model (GPDM). We introduce a kernelised version of GPDM for a more expressive covariance structure between both the observable and latent coordinates. We combine the approach with transfer learning to track the future state-of-health up to end-of-life. The method can incorporate features as different physical observables, without requiring their values beyond the time up to which data is available. Transfer learning is used to improve learning of the hyperparameters using data from similar batteries. The accuracy and superiority of the approach over modern benchmarks algorithms including a Gaussian process model and deep convolutional and recurrent networks are demonstrated on three data sets, particularly at the early stages of the battery lifetime.