We study several versions of the Schmidt–Kennicutt (SK) relation obtained for isolated spiral galaxies in TreeSPH simulations run with the gadget3 code including the novel MUlti-Phase Particle Integrator (muppi) algorithm for star formation and stellar feedback. This is based on a subresolution multiphase treatment of gas particles, where star formation is explicitly related to molecular gas, and the fraction of gas in the molecular phase is computed from hydrodynamical pressure, following a phenomenological correlation. No chemical evolution is included in this version of the code. The standard SK relation between surface densities of cold (neutral+molecular) gas and star formation rate of simulated galaxies shows a steepening at low gas surface densities, starting from a knee whose position depends on disc gas fraction: for more gas-rich discs, the steepening takes place at higher surface densities. Because gas fraction and metallicity are typically related, this environmental dependence mimics the predictions of models where the formation of H2 is modulated by metallicity. The cold gas surface density at which H i and molecular gas surface densities equate can range from ∼10 up to 34 M⊙ pc−2. As expected, the SK relation obtained using molecular gas shows much smaller variations among simulations. We find that disc pressure is not well represented by the classical external pressure of a disc in vertical hydrostatic equilibrium. Instead, it is well fit by the expression Pfit=Σcoldσcoldκ/6, where the three quantities on the right-hand side are cold gas surface density, vertical velocity dispersion and epicyclic frequency. When the ‘dynamical’ SK relation, i.e. the relation that uses gas surface density divided by orbital time, is considered, we find that all of our simulations stay on the same relation. We interpret this as a manifestation of the equilibrium between energy injection and dissipation in stationary galaxy discs, when energetic feedback is effective and pressure is represented by the expression given above. These findings further support the idea that a realistic model of the structure of galaxy discs should take into account energy injection by supernovae.