Machine learning in medical imaging during clinical routine is impaired by changes in scanner protocols, hardware, or policies resulting in a heterogeneous set of acquisition settings. When training a deep learning model on an initial static training set, model performance and reliability suffer from changes of acquisition characteristics as data and targets may become inconsistent. Continual learning can help to adapt models to the changing environment by training on a continuous data stream. However, continual manual expert labelling of medical imaging requires substantial effort. Thus, ways to use labelling resources efficiently on a well chosen sub-set of new examples is necessary to render this strategy feasible. Here, we propose a method for continual active learning operating on a stream of medical images in a multi-scanner setting. The approach automatically recognizes shifts in image acquisition characteristics - new domains -, selects optimal examples for labelling and adapts training accordingly. Labelling is subject to a limited budget, resembling typical real world scenarios. To demonstrate generalizability, we evaluate the effectiveness of our method on three tasks: cardiac segmentation, lung nodule detection and brain age estimation. Results show that the proposed approach outperforms other active learning methods, while effectively counteracting catastrophic forgetting.