Many current neural networks for medical imaging generalise poorly to data unseen during training. Such behaviour can be caused by networks overfitting easy-to-learn, or statistically dominant, features while disregarding other potentially informative features. For example, indistinguishable differences in the sharpness of the images from two different scanners can degrade the performance of the network significantly. All neural networks intended for clinical practice need to be robust to variation in data caused by differences in imaging equipment, sample preparation and patient populations. To address these challenges, we evaluate the utility of spectral decoupling as an implicit bias mitigation method. Spectral decoupling encourages the neural network to learn more features by simply regularising the networks' unnormalised prediction scores with an L2 penalty, thus having no added computational costs. We show that spectral decoupling allows training neural networks on datasets with strong spurious correlations and increases networks' robustness for data distribution shifts. To validate our findings, we train networks with and without spectral decoupling to detect prostate cancer tissue slides and COVID-19 in chest radiographs. Networks trained with spectral decoupling achieve up to 9.5 percent point higher performance on external datasets. Our results show that spectral decoupling helps with generalisation issues associated with neural networks, and can be used to complement or replace computationally expensive explicit bias mitigation methods, such as stain normalization in histological images. We recommend using spectral decoupling as an implicit bias mitigation method in any neural network intended for clinical use.