The magnetic structure of the hexagonal polymorph of FeGe has been investigated by means of neutron diffraction on single crystals at low temperature and for magnetic fields applied perpendicular to the c axis. Between 410 and approximately 55K the magnetic structure is collinear c-axis antiferromagnetic. Below approximately 55K the structure changes to c-axis double-cone antiferromagnetic with an inter-layer turn angle for the basal-plane moment component of 194.4 degrees , independent of temperature and applied field. The cone half-angle increases with decreasing temperature to approximately 14 degrees at 4.2K, but its temperature dependence shows a pronounced kink at 30K, indicating a phase change at this temperature. At 4.2K the authors observe an anomalous decrease of the basal-plane moment component at a critical field (B perpendicular to c) of 1.4 T. As the temperature is increased the critical field decreases and the anomaly becomes less pronounced. The cone structure is found to persist up at least 3.9 T, which was the upper limit of the applied field. The neutron diffraction data are discussed and related to previously published macroscopic data (e.g. magnetic susceptibility, torsion and Mossbauer data) as well as to earlier neutron diffraction results.