Microbes live in ever-changing environments where they need to adapt their metabolism to different nutrient conditions. Many studies have characterized the response of genetically identical cells to nutrient switches in homogeneous cultures; however, in nature, microbes often live in spatially structured groups such as biofilms where cells can create metabolic gradients by consuming and releasing nutrients. Consequently, cells experience different local microenvironments and vary in their phenotype. How does this phenotypic variation affect the ability of cells to cope with nutrient switches? Here, we address this question by growing dense populations of Escherichia coli in microfluidic chambers and studying a switch from glucose to acetate at the single-cell level. Before the switch, cells vary in their metabolic activity: some grow on glucose, while others cross-feed on acetate. After the switch, only few cells can resume growth after a period of lag. The probability to resume growth depends on a cells' phenotype prior to the switch: it is highest for cells cross-feeding on acetate, while it depends in a non-monotonic way on the growth rate for cells growing on glucose. Our results suggest that the strong phenotypic variation in spatially structured populations might enhance their ability to cope with fluctuating environments.