High-pressure single-crystal X-ray diffraction at ambient temperature and high-pressure SQUID measurements down to 2 K were performed up to ∼2.5 GPa on ammonium metal formates, [NH4][M(HCOO)3] where M = Mn2+, Fe2+, and Ni2+, in order to correlate structural variations to magnetic behaviour. Similar structural distortions and phase transitions were observed for all compounds, although the transition pressures varied with the size of the metal cation. The antiferromagnetic ordering in [NH4][M(HCOO)3] compounds was maintained as a function of pressure, and the magnetic ordering transition temperature changed within a few kelvins depending on the structural distortion and the metal cation involved. These compounds, in particular [NH4][Fe(HCOO)3], showed greatest sensitivity to the degree of spin canting upon compression, clearly visible from the twenty-fold increase in the low-temperature magnetisation for [NH4][Fe(HCOO)3] at 1.4 GPa, and the change from purely antiferromagnetic to weakly ferromagnetic ordering in [NH4][Mn(HCOO)3] at 1 GPa. The variation in the exchange couplings and spin canting was checked with density-functional calculations that reproduce well the increase in canted moment within [NH4][Fe(HCOO)3] upon compression, and suggest that the Dzyaloshinskii-Moriya (DM) interaction is evolving as a function of pressure. The pressure dependence of spin canting is found to be highly dependent on the metal cation, as magnetisation magnitudes did not change significantly for when M = Ni2+ or Mn2+. These results demonstrate that the overall magnetic behaviour of each phase upon compression was not only dependent on the structural distortions but also on the electronic configuration of the metal cation.