Background – While language impairment is the defining symptom of aphasia, the co-occurrence of non-language cognitive deficits and their importance in predicting rehabilitation and recovery outcomes is well documented. However, few studies have explored how individual cognitive domains contribute to patients′ impairment and how this relates to underlying lesion pattern. A better understanding of this is essential for improving aphasia treatments. Objectives – This study aimed to explore the brain-behaviour relationships between tests of individual cognitive skill, as well as language abilities, in patients with post-stroke aphasia. We predicted our analysis would reveal a latent (non-language specific) cognitive component, which would be driven by damage to left frontal cortices. Methods – We analysed the behavioural and neural correlates of an extensive battery of language and non-language cognitive tests in a selective sample of 36 patients with post-stroke anomic aphasia, with relatively intact speech comprehension and repetition. The behavioural variables were analysed using Principle Component Analysis and their neural correlates were estimated using Voxel-Based Correlational Morphology. Results – A significant number of anomia patients showed impaired performance on tests of non-language cognitive function. The variance underlying behavioural performance was best captured by four orthogonal components, two non-language cognitive components (executive function and verbal working memory) and two previously identified language components (phonology and semantics). Brain-behaviour relationships revealed separable neural correlates for each component in line with previous studies and a novel executive function correlate in the left inferior frontal cortex (LIFC). Conclusion – Our findings suggest that in patients with chronic post-stroke anomia, non-language cognitive abilities explain more of the variance in language function than classical models of the condition imply. Additionally, lesions to the LIFC, including Broca′s area, were associated with executive (dys)function, independent of language abilities, suggesting that lesions to this area might be primarily driving a (non-language specific) cognitive component in anomia.