Batteries are rapidly shifting the transport paradigm from fossil fuels to renewable energy. Accurately predicting their ageing trajectory and remaining useful life is not only required to ensure safe and reliable operation of electric vehicles (EVs) but is also the fundamental step toward health-conscious use and residual value assessment of the battery. However, battery degradation results from diverse, interlaced, and nonlinear degradation mechanisms that made battery life prediction a challenging task. In this work, we propose a histogram data-based framework for online adaptive prediction of battery ageing trajectory and lifetime under generalised conditions. A sufficiently general procedure for feature construction is first built up that involves two-step data compression and uses a range of statistical properties of the histogram data. From the constructed comprehensive feature pool, a feature dependence check-and-control scheme is then designed to select the most relevant and independent features. Based on the selected features, we develop a library of global models associated with different machine learning methods and then intelligently adapt them online for individualised prediction. Finally, our framework is trained and tested on three large datasets, with one being measured from 7296 plug-in hybrid EVs. While the best global models achieve 0.93% test error on laboratory data and 1.41% test error on the real-world fleet data, the adaptation algorithm further reduces the errors by up to 13.7%, all requiring low computational power and memory. This work proves the feasibility and benefits of using histogram data and highlights the importance of online adaptation for predicting the behaviour of complex dynamic systems.