Unlike crystals, glasses age or devitrify over time to lower their free energy, reflecting their intrinsically non-equilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that devitrification and ageing of quasi hard-sphere glasses are prevented by suppressing volume-fraction inhomogeneities in the spatial arrangement of the particles. A glass of monodisperse quasi hard-sphere particles, known to devitrify and age with `avalanche-like intermittent dynamics, is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this almost entirely prevents structural relaxation and devitrification even in the presence of crystallites. The homogenisation of local volume fractions leads to a dramatic change in the local mechanical environment of each particle, with a clear homogenisation in the number of load-bearing nearest neighbours each particle has. This indicates that we may stabilise glasses by making them more `mechanically homogeneous. Our finding provides a physical principle for glass stabilisation and opens a novel route to the formation of mechanically stabilised glasses.