M 87 is one of the closest (z = 0.004 36) extragalactic sources emitting at very high energies (VHE, E > 100 GeV). The aim of this work is to locate the region of the VHE gamma-ray emission and to describe the observed broad-band spectral energy distribution (SED) during the low VHE gamma-ray state. The data from M 87 collected between 2012 and 2015 as part of a MAGIC monitoring programme are analysed and combined with multiwavelength data from Fermi-LAT, Chandra, HST, EVN, VLBA, and the Liverpool Telescope. The averaged VHE gamma-ray spectrum can be fitted from ̃100 GeV to ̃10 TeV with a simple power law with a photon index of (-2.41 ± 0.07), while the integral flux above 300 GeV is (1.44± 0.13)× 10^{-12} cm^{-2} s^{-1}. During the campaign between 2012 and 2015, M 87 is generally found in a low-emission state at all observed wavelengths. The VHE gamma-ray flux from the present 2012-2015M 87 campaign is consistent with a constant flux with some hint of variability (̃ 3 σ) on a daily time-scale in 2013. The low-state gamma-ray emission likely originates from the same region as the flare-state emission. Given the broad-band SED, both a leptonic synchrotron self-Compton and a hybrid photohadronic model reproduce the available data well, even if the latter is preferred. We note, however, that the energy stored in the magnetic field in the leptonic scenario is very low, suggesting a matter-dominated emission region.