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 around the world. For many neurological conditions, this delay can result in increased morbidity and mortality. An automated triaging tool could reduce reporting times for abnormal examinations by identifying abnormalities at the time of imaging and prioritizing the reporting of these scans. In this work, we present a convolutional neural network for detecting clinically-relevant abnormalities in $\text{T}_2$-weighted head MRI scans. Using a validated neuroradiology report classifier, we generated a labelled dataset of 43,754 scans from two large UK hospitals for model training, and demonstrate accurate classification (area under the receiver operating curve (AUC) = 0.943) on a test set of 800 scans labelled by a team of neuroradiologists. Importantly, when trained on scans from only a single hospital the model generalized to scans from the other hospital ($\Delta$AUC $\leq$ 0.02). A simulation study demonstrated that our 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 hospitals, demonstrating feasibility for use in a clinical triage environment.