It has been hypothesized that complex englacial structures identified within the East Antarctic and Greenland ice sheets are generated by (i) water freezing to the ice sheet base and evolving under ice flow, (ii) deformation of ice of varying rheology, or (iii) entrainment of basal material. Using ice-penetrating radar, we identify a widespread complex of deep-ice facies in West Antarctica that exist in the absence of basal water. These deep-ice units are extensive, thick (>500 m), and incorporate multiple highly reflective englacial layers. At the lateral margin of an enhanced flow tributary of the Institute Ice Stream, these units are heavily deformed and folded by the action of lateral flow convergence. Radar reflectivity analysis demonstrates that the uppermost reflector of the deep-ice package is highly anisotropic, due to abrupt alternations in crystal orientation fabric, and consequently will have a different rheology to the ice above and below it. Deformation and folding of the deep-ice package is an englacial response to the combination of laterally-convergent ice flow and the physical properties of the ice column.