Leukaemia is a dysfunction that affects the production of white blood cells in the bone marrow. Young cells are abnormally produced, replacing normal blood cells. Consequently, the person suffers problems in transporting oxygen and in fighting infections. This article proposes a convolutional neural network (CNN) named LeukNet that was inspired on convolutional blocks of VGG-16, but with smaller dense layers. To define the LeukNet parameters, we evaluated different CNNs models and fine-tuning methods using 18 image datasets, with different resolution, contrast, colour and texture characteristics. We applied data augmentation operations to expand the training dataset, and the 5-fold cross-validation led to an accuracy of 98.61%. To evaluate the CNNs generalisation ability, we applied a cross-dataset validation technique. The obtained accuracies using cross-dataset experiments on three datasets were 97.04, 82.46 and 70.24%, which overcome the accuracies obtained by current state-of-the-art methods. We conclude that using the most common and deepest CNNs may not be the best choice for applications where the images to be classified differ from those used in pre-training. Additionally, the adopted cross-dataset validation approach proved to be an excellent choice to evaluate the generalisation capability of a model, as it considers the model performance on unseen data, which is paramount for CAD systems.