ABSTRACT The α-element abundances of the globular cluster (GC) and field star populations of galaxies encode information about the formation of each of these components. We use the E-MOSAICS cosmological simulations of ∼L* galaxies and their GCs to investigate the [α/Fe]–[Fe/H] distribution of field stars and GCs in 25 Milky Way–mass galaxies. The [α/Fe]–[Fe/H] distribution of GCs largely follows that of the field stars and can also therefore be used as tracers of the [α/Fe]–[Fe/H] evolution of the galaxy. Due to the difference in their star formation histories, GCs associated with stellar streams (i.e. which have recently been accreted) have systematically lower [α/Fe] at fixed [Fe/H]. Therefore, if a GC is observed to have low [α/Fe] for its [Fe/H] there is an increased possibility that this GC was accreted recently alongside a dwarf galaxy. There is a wide range of shapes for the field star [α/Fe]–[Fe/H] distribution, with a notable subset of galaxies exhibiting bimodal distributions, in which the high [α/Fe] sequence is mostly comprised of stars in the bulge, a high fraction of which are from disrupted GCs. We calculate the contribution of disrupted GCs to the bulge component of the 25 simulated galaxies and find values between 0.3 and 14 per cent, where this fraction correlates with the galaxy’s formation time. The upper range of these fractions is compatible with observationally inferred measurements for the Milky Way, suggesting that in this respect the Milky Way is not typical of L*galaxies, having experienced a phase of unusually rapid growth at early times.