Understanding the mechanisms by which climate variation can drive population changes requires information linking climate, local conditions, trophic resources, behaviour and demography. Climate change alters the seasonal pattern of emergence and abundance of invertebrate populations, which may have important consequences for the breeding performance and population change of insectivorous birds. In this study, we examine the role of food availability in driving behavioural changes in an insectivorous migratory songbird; the Eurasian reed warbler Acrocephalus scirpaceus. We use a feeding experiment to examine the effect of increased food supply on different components of breeding behaviour and first-brood productivity, over three breeding seasons (2012-2014). Reed warblers respond to food-supplementation by advancing their laying date by up to 5.6 days. Incubation periods are shorter in supplemented groups during the warmest mean spring temperatures. Nestling growth rates are increased in nests provisioned by supplemented parents. In addition, nest predation is reduced, possibly because supplemented adults spend more time at the nest and faster nestling growth reduces the period of vulnerability of eggs and nestlings to predators (and brood parasites). The net effect of these changes is to advance the fledging completion date and to increase the overall productivity of the first brood for supplemented birds. European populations of reed warblers are currently increasing; our results suggest that advancing spring phenology, leading to increased food availability early in the breeding season, could account for this change by facilitating higher productivity. Furthermore, the earlier brood completion potentially allows multiple breeding attempts. This study identifies the likely trophic and behavioural mechanisms by which climate-driven changes in invertebrate phenology and abundance may lead to changes in breeding phenology, nest survival and net reproductive performance of insectivorous birds.