White matter hyperintensities (WMH) and ischaemic stroke lesions (ISL) are key imaging biomarkers of cerebral small vessel disease (SVD) detectable on magnetic resonance imaging (MRI). The development of robust deep learning models to automatically segment and differentiate these pathologies remains challenging. Specifically, WMH and ISL frequently co-occur within the same subject and present as visually confounding hyperintensities on fluid-attenuated inversion recovery (FLAIR) sequences, complicating their accurate delineation. To address the scarcity of fully annotated cohorts, we systematically evaluated six accessible strategies for training a joint WMH and ISL segmentation model using partially labelled data. We aggregated privately held and publicly available datasets to curate a large-scale cohort of 2,052 MRI volumes, of which 1341 and 1152 volumes contained ground truth annotations for WMH and ISL, respectively. Our analysis indicates that multiple strategies effectively leverage partially labelled data to enhance overall model performance, with pseudolabelling emerging as the most effective approach. This model exhibited a consistent WMH segmentation policy and successfully detected the majority of FLAIR-positive ISL. These findings demonstrate the viability of using partially labelled data to develop reliable automated segmentation tools, which can support ongoing SVD monitoring and high-throughput biomarker extraction for large-scale clinical research.