Positive feedback plays a major role in the emergence of many collective animal behaviours. In many ants pheromone trails recruit and direct nestmate foragers to food sources. The strong positive feedback caused by trail pheromones allows fast collective responses but can compromise flexibility. Previous laboratory experiments have shown that when the environment changes, colonies are often unable to reallocate their foragers to a more rewarding food source. Here we show both experimentally, using colonies of Lasius niger, and with an agent-based simulation model, that negative feedback caused by crowding at feeding sites allows ant colonies to maintain foraging flexibility even with strong recruitment to food sources. In a constant environment, negative feedback prevents the frequently found bias towards one feeder (symmetry breaking) and leads to equal distribution of foragers. In a changing environment, negative feedback allows a colony to quickly reallocate the majority of its foragers to a superior food patch that becomes available when foraging at an inferior patch is already well underway. The model confirms these experimental findings and shows that the ability of colonies to switch to a superior food source does not require the decay of trail pheromones. Our results help to resolve inconsistencies between collective foraging patterns seen in laboratory studies and observations in the wild, and show that the simultaneous action of negative and positive feedback is important for efficient foraging in mass-recruiting insect colonies.