The contribution of the majority of frequently mutated genes to tumourigenesis is not fully defined. Many aggressive human cancers, such as triple negative breast cancers (TNBCs), have a poor prognosis and lack tractable biomarkers and targeted therapeutic options. Here, we systematically characterize loss-of-function mutations to generate a functional map of novel driver genes in a 3-dimensional model of breast cancer heterogeneity that more readily recapitulates the unfavourable tumour microenvironment in vivo. This identified the histone acetyltransferase CREBBP as a potent tumour suppressor gene whose silencing provided a 3D-specific growth advantage only under oxygen and nutrient deplete conditions. CREBBP protein expression was altered in a substantial proportion of TNBCs as well as several other solid tumours, including endometrial, bladder, ovarian and squamous lung cancers. In multiple primary tumours and cell models, loss of CREBBP activity resulted in upregulation of the FOXM1 transcriptional network. Strikingly, treatment with a range of CDK4/6 inhibitors (CDK4/6i), that indirectly target FOXM1 activity, selectively impaired growth in both CREBBP-altered spheroids and cell line xenografts and patient derived models from multiple tumour types. This study is the first to provide rationale for CREBBP as a biomarker for CDK4/6i response in cancer representing a new treatment paradigm for tumours that harbour CREBBP alterations that have limited therapeutic options.