This paper describes a methodology that extracts key morphological features from histological breast cancer images in order to automatically assess Tumour Cellularity (TC) in Neo-Adjuvant treatment (NAT) patients. The response to NAT gives information on therapy efficacy and it is measured by the residual cancer burden index, which is composed of two metrics: TC and the assessment of lymph nodes. The data consist of whole slide images (WSIs) of breast tissue stained with Hematoxylin and Eosin (H&E) released in the 2019 SPIE Breast Challenge. The methodology proposed is based on traditional computer vision methods (K-means, watershed segmentation, Otsu’s binarisation, and morphological operations), implementing colour separation, segmentation, and feature extraction. Correlation between morphological features and the residual TC after a NAT treatment was examined. Linear regression and statistical methods were used and twenty-two key morphological parameters from the nuclei, epithelial region, and the full image were extracted. Subsequently, an automated TC assessment that was based on Machine Learning (ML) algorithms was implemented and trained with only selected key parameters. The methodology was validated with the score assigned by two pathologists through the intra-class correlation coefficient (ICC). The selection of key morphological parameters improved the results reported over other ML methodologies and it was very close to deep learning methodologies. These results are encouraging, as a traditionally-trained ML algorithm can be useful when limited training data are available preventing the use of deep learning approaches.