It is widely assumed that cognitive functions decline with age and that these decrements are associated with age-related changes in patterns of functional activity. However, these functional changes may be due to age-related increased responsiveness to task demands and not to other cognitive processes on which neural and behavioural responses rely, since many ageing studies use task paradigms that may not be orthogonal to the cognitive function being investigated. Here we test this hypothesis in adults aged 20–86 years by combining measures of language comprehension, functional connectivity and neural integrity to identify functional networks activated in two language experiments with varying task demands. In one, participants listened to spoken sentences without performing an overt task (the natural listening condition) while in the other they performed a task in response to the same sentences. Using task-based ICA of fMRI, we identified a left-lateralised frontotemporal network associated with syntactic analysis, which remained consistently activated regardless of task demands. In contrast, in the task condition only a separate set of components showed task-specific activity in Opercular, Frontoparietal, and bilateral PFC. Only the PFC showed age-related increases in activation which, furthermore, was strongly mediated by grey matter health. These results suggest that, contrary to prevailing views, age-related changes in cognitive activation may be due in part to differential responses to task-related processes.