Radio signal recognition is a crucial function in electronic warfare. Precise identification and localisation of radar pulse activities are required by electronic warfare systems to produce effective countermeasures. Despite the importance of these tasks, deep learning-based radar pulse activity recognition methods have remained largely underexplored. While deep learning for radar modulation recognition has been explored previously, classification tasks are generally limited to short and non-interleaved IQ signals, limiting their applicability to military applications. To address this gap, we introduce an end-to-end multi-stage learning approach to detect and localise pulse activities of interleaved radar signals across an extended time horizon. We propose a simple, yet highly effective multi-stage architecture for incrementally predicting fine-grained segmentation masks that localise radar pulse activities across multiple channels. We demonstrate the performance of our approach against several reference models on a novel radar dataset, while also providing a first-of-its-kind benchmark for radar pulse activity segmentation.