Algorithmic segmentation of histologically relevant regions of tissues in digitized histopathological images is a critical step towards computer-assisted diagnosis and analysis. For example, automatic identification of epithelial and stromal tissues in images is important for spatial localisation and guidance in the analysis and characterisation of tumour micro-environment. Current segmentation approaches are based on supervised methods, which require extensive training data from high quality, manually annotated images. This is often difficult and costly to obtain. This paper presents an alternative data-independent framework based on unsupervised segmentation of oropharyngeal cancer tissue micro-arrays (TMAs). An automated segmentation algorithm based on mathematical morphology is first applied to light microscopy images stained with haematoxylin and eosin. This partitions the image into multiple binary ‘virtual-cells’, each enclosing a potential ‘nucleus’ (dark basins in the haematoxylin absorbance image). Colour and morphology measurements obtained from these virtual-cells as well as their enclosed nuclei are input into an advanced unsupervised learning model for the identification of epithelium and stromal tissues. Here we exploit two Consensus Clustering (CC) algorithms for the unsupervised recognition of tissue compartments, that consider the consensual opinion of a group of individual clustering algorithms. Unlike most unsupervised segmentation analyses, which depend on a single clustering method, the CC learning models allow for more robust and stable detection of tissue regions. The proposed framework performance has been evaluated on fifty-five hand-annotated tissue images of oropharyngeal tissues. Qualitative and quantitative results of the proposed segmentation algorithm compare favourably with eight popular tissue segmentation strategies. Furthermore, the unsupervised results obtained here outperform those obtained with individual clustering algorithms.