Iron(IV) oxides are strongly correlated materials with negative charge-transfer energy (negative \ensuremath{\Delta}), and exhibit peculiar electronic and magnetic properties such as topological helical spin structures in the metallic cubic perovskite ${\mathrm{SrFeO}}_{3}$. Here, the spin structure of the layered negative-\ensuremath{\Delta} insulator ${\mathrm{Sr}}_{2}{\mathrm{FeO}}_{4}$ was studied by powder neutron diffraction in zero field and magnetic fields up to 6.5 T. Below ${T}_{\mathrm{N}}=56\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, ${\mathrm{Sr}}_{2}{\mathrm{FeO}}_{4}$ adopts an elliptical cycloidal spin structure with modulated magnetic moments between 1.9 and 3.5 ${\ensuremath{\mu}}_{\mathrm{B}}$ and a propagation vector $\mathbit{k}=(\ensuremath{\tau},\ensuremath{\tau},0)$ with $\ensuremath{\tau}=0.137$. With increasing magnetic field the spin structure undergoes a spin-flop transition near 5 T. Synchrotron $^{57}\mathrm{Fe}$-M\"ossbauer 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 ${\mathrm{K}}_{2}{\mathrm{NiF}}_{4}$-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.