Supervised machine learning-based medical image computing applications necessitate expert label curation, while unlabelled image data might be relatively abundant. Active learning methods aim to prioritise a subset of available image data for expert annotation, for label-efficient model training. We develop a controller neural network that measures priority of images in a sequence of batches, as in batch-mode active learning, for multi-class segmentation tasks. The controller is optimised by rewarding positive task-specific performance gain, within a Markov decision process (MDP) environment that also optimises the task predictor. In this work, the task predictor is a segmentation network. A meta-reinforcement learning algorithm is proposed with multiple MDPs, such that the pre-trained controller can be adapted to a new MDP that contains data from different institutes and/or requires segmentation of different organs or structures within the abdomen. We present experimental results using multiple CT datasets from more than one thousand patients, with segmentation tasks of nine different abdominal organs, to demonstrate the efficacy of the learnt prioritisation controller function and its cross-institute and cross-organ adaptability. We show that the proposed adaptable prioritisation metric yields converging segmentation accuracy for the novel class of kidney, unseen in training, using between approximately 40\% to 60\% of labels otherwise required with other heuristic or random prioritisation metrics. For clinical datasets of limited size, the proposed adaptable prioritisation offers a performance improvement of 22.6\% and 10.2\% in Dice score, for tasks of kidney and liver vessel segmentation, respectively, compared to random prioritisation and alternative active sampling strategies.