During mouse development, core planar cell polarity (PCP) proteins become polarized in the epidermal plane to guide angling/morphogenesis of hair follicles. How PCP is established is poorly understood. Here, we identify a key role for Wdr1 (also known as Aip1), an F-actin-binding protein that enhances cofilin/destrin-mediated F-actin disassembly. We show that cofilin and destrin function redundantly in developing epidermis, but their combined depletion perturbs cell adhesion, cytokinesis, apicobasal polarity and PCP. Although Wdr1 depletion accentuates single-loss-of-cofilin/destrin phenotypes, alone it resembles core PCP mutations. Seeking a mechanism, we find that Wdr1 and cofilin/destrin-mediated actomyosin remodelling are essential for generating or maintaining cortical tension within the developing epidermal sheet and driving the cell shape and planar orientation changes that accompany establishment of PCP in mammalian epidermis. Our findings suggest intriguing evolutionary parallels but mechanistic modifications to the distal wing hinge-mediated mechanical forces that drive cell shape change and orient PCP in the Drosophila wing disc.