Recognising human activities from streaming videos poses unique challenges to learning algorithms: predictive models need to be scalable, incrementally trainable, and must remain bounded in size even when the data stream is arbitrarily long. Furthermore, as parameter tuning is problematic in a streaming setting, suitable approaches should be parameterless, and make no assumptions on what class labels may occur in the stream. We present here an approach to the recognition of human actions from streaming data which meets all these requirements by: (1) incrementally learning a model which adaptively covers the feature space with simple local classifiers; (2) employing an active learning strategy to reduce annotation requests; (3) achieving promising accuracy within a fixed model size. Extensive experiments on standard benchmarks show that our approach is competitive with state-of-the-art non-incremental methods, and outperforms the existing active incremental baselines.