Accurate tumour segmentation is vital for various targeted diagnostic and therapeutic procedures for cancer, e.g., planning biopsies or tumour ablations. Manual delineation is extremely labour-intensive, requiring substantial expert time. Fully-supervised machine learning models aim to automate such localisation tasks, but require a large number of costly and often subjective 3D voxel-level labels for training. The high-variance and subjectivity in such labels impacts model generalisability, even when large datasets are available. Histopathology labels may offer more objective labels but the infeasibility of acquiring pixel-level annotations to develop tumour localisation methods based on histology remains challenging in-vivo. In this work, we propose a novel weakly-supervised semantic segmentation framework called SPARS (Self-Play Adversarial Reinforcement Learning for Segmentation), which utilises an object presence classifier, trained on a small number of image-level binary cancer presence labels, to localise cancerous regions on CT scans. Such binary labels of patient-level cancer presence can be sourced more feasibly from biopsies and histopathology reports, enabling a more objective cancer localisation on medical images. Evaluating with real patient data, we observed that SPARS yielded a mean dice score of $77.3 \pm 9.4$, which outperformed other weakly-supervised methods by large margins. This performance was comparable with recent fully-supervised methods that require voxel-level annotations. Our results demonstrate the potential of using SPARS to reduce the need for extensive human-annotated labels to detect cancer in real-world healthcare settings.