Iron(IV) oxides are strongly correlated materials with negative charge-transfer energy (negative Δ), and exhibit peculiar electronic and magnetic properties such as topological helical spin structures in the metallic cubic perovskite SrFeO3. Here, the spin structure of the layered negative-Δ insulator Sr2FeO4 was studied by powder neutron diffraction in zero field and magnetic fields up to 6.5 T. Below TN=56K, Sr2FeO4 adopts an elliptical cycloidal spin structure with modulated magnetic moments between 1.9 and 3.5 μB and a propagation vector k=(τ,τ,0) with τ=0.137. With increasing magnetic field the spin structure undergoes a spin-flop transition near 5 T. Synchrotron 57Fe-Mössbauer spectroscopy reveals that the spin spiral transforms to a ferromagnetic structure at pressures between 5 and 8 GPa, just in the pressure range where a Raman-active phonon nonintrinsic to the K2NiF4-type crystal structure vanishes. These results indicate an insulating ground state which is stabilized by a hidden structural distortion and differs from the charge disproportionation in other Fe(IV) oxides.