Individuals respond adaptively to their environment. Yet, they may differ in their responses even when confronted with the same environmental challenge. Several complementary conceptual frameworks suggest that within populations among-individual variation in life history strategies aligns not only with individuals' propensities to take risks across different situations but also with their sensitivity to variation in environmental cues. Risk-prone individuals, suggested to invest more in current reproduction at the cost of their future reproductive prospects, are predicted to be less sensitive to environmental variation than risk-averse individuals. We tested this prediction in a population of breeding blue tits, Cyanistes caeruleus, by confronting them with different levels of predation threat at their nests and recording their latency to resume brood provisioning after the removal of the predator stimulus. We presented taxidermic woodpecker, Dendrocopos major (a common brood predator) and sparrowhawk, Accipiter nisus (a common adult predator) mounts at each nest, respectively representing low and high levels of threat to adult blue tits. As a nonpredator control stimulus, we presented a blackbird, Turdus merula, mount. We found that on average parents took longer to resume provisioning after presentation of a sparrowhawk than a woodpecker or blackbird. Furthermore, individual latency responses across all threat levels taken together were repeatable. However, despite the population level plastic adjustment to the level of predation threat, we found no evidence for among-individual variation in plasticity. Instead, individual differences in responses were roughly maintained across all levels of threat. While our findings show that individuals differ in their level of risk taking, in the high-stakes and ecologically relevant context of predation risk during parental care, commonly held expectations about among-individual variation in behavioural plasticity were not met.