One of the key tissue movements driving closure of a wound is re-epithelialisation. Earlier wound healing studies describe the dynamic cell behaviours that contribute to wound re-epithelialisation, including cell division, cell shape changes and cell migration, as well as the signals that might regulate these cell behaviours. Here, we have used a series of deep learning tools to quantify the contributions of each of these cell behaviours from movies of repairing wounds in the Drosophila pupal wing epithelium. We test how each is altered after knockdown of the conserved wound repair signals Ca2+ and JNK, as well as after ablation of macrophages that supply growth factor signals believed to orchestrate aspects of the repair process. Our genetic perturbation experiments provide quantifiable insights regarding how these wound signals impact cell behaviours. We find that Ca2+ signalling is a master regulator required for all contributing cell behaviours; JNK signalling primarily drives cell shape changes and divisions, whereas signals from macrophages largely regulate cell migration and proliferation. Our studies show deep learning to be a valuable tool for unravelling complex signalling hierarchies underlying tissue repair.