The COVID-19 pandemic has inspired unprecedented data collection and computer vision modelling efforts worldwide, focused on the diagnosis of COVID-19 from medical images. However, these models have found limited, if any, clinical application due in part to unproven generalization to data sets beyond their source training corpus. This study investigates the generalizability of deep learning models using publicly available COVID-19 Computed Tomography data through cross dataset validation. The predictive ability of these models for COVID-19 severity is assessed using an independent dataset that is stratified for COVID-19 lung involvement. Each inter-dataset study is performed using histogram equalization, and contrast limited adaptive histogram equalization with and without a learning Gabor filter. We show that under certain conditions, deep learning models can generalize well to an external dataset with F1 scores up to 86%. The best performing model shows predictive accuracy of between 75% and 96% for lung involvement scoring against an external expertly stratified dataset. From these results we identify key factors promoting deep learning generalization, being primarily the uniform acquisition of training images, and secondly diversity in CT slice position.