The growing demand for head magnetic resonance imaging (MRI) examinations, along with a global shortage of radiologists, has led to an increase in the time taken to report head MRI scans in recent years. For many neurological conditions, this delay can result in poorer patient outcomes and inflated healthcare costs. Potentially, computer vision models could help reduce reporting times for abnormal examinations by flagging abnormalities at the time of imaging, allowing radiology departments to prioritise limited resources into reporting these scans first. To date, however, the difficulty of obtaining large, clinically-representative labelled datasets has been a bottleneck to model development. In this work, we present a deep learning framework, based on convolutional neural networks, for detecting clinically-relevant abnormalities in minimally processed, hospital-grade axial T2-weighted and axial diffusion-weighted head MRI scans. The models were trained at scale using a Transformer-based neuroradiology report classifier to generate a labelled dataset of 70,206 examinations from two large UK hospital networks, and demonstrate fast (< 5 s), accurate (area under the receiver operating characteristic curve (AUC) > 0.9), and interpretable classification, with good generalisability between hospitals (ΔAUC ≤ 0.02). Through a simulation study we show that our best model would reduce the mean reporting time for abnormal examinations from 28 days to 14 days and from 9 days to 5 days at the two hospital networks, demonstrating feasibility for use in a clinical triage environment.