Functional connectivity within and between Intrinsic Connectivity Networks (ICNs) transforms over development and is thought to support high order cognitive functions. But how variable is this process, and does it diverge with altered cognitive development? We investigated age-related changes in integration and segregation within and between ICNs in neurodevelopmentally 'at-risk' children, identified by practitioners as experiencing cognitive difficulties in attention, learning, language, or memory. In our analysis we used performance on a battery of 10 cognitive tasks alongside resting-state functional magnetic resonance imaging in 175 at-risk children and 62 comparison children aged 5-16. We observed significant age-by-group interactions in functional connectivity between two network pairs. Integration between the ventral attention and visual networks and segregation of the limbic and fronto-parietal networks increased with age in our comparison sample, relative to at-risk children. Furthermore, functional connectivity between the ventral attention and visual networks in comparison children significantly mediated age-related improvements in executive function, compared to at-risk children. We conclude that integration between ICNs show divergent neurodevelopmental trends in the broad population of children experiencing cognitive difficulties, and that these differences in functional brain organisation may partly explain the pervasive cognitive difficulties within this group over childhood and adolescence. [This article was written with the CALM Team.]