The halo and disc globular cluster population can be used as a tracer of the primordial epochs of the Milky Way formation. In this work, literature data of globular clusters ages, chemical abundances, and structural parameters are studied, explicitly focussing on the origin of the known split in the age-metallicity relation (AMR) of globular clusters. When the α-element abundances, which are less strongly affected by the internal light-element spread of globular clusters (Si, Ca), are considered, a very low observational scatter among metal-poor clusters is observed. A plateau at [SiCa/Fe],∼ 0.35 dex, with a dispersion of only 0.05 dex (including abundance errors) is observed up to a metallicity of about −0.75 dex. Only a few metal-poor clusters in this metallicity interval present low [SiCa/Fe] abundances. Moreover, metal-rich globular clusters show a knee in the [α/Fe] vs. [Fe/H] plane around [Fe/H] ∼ −0.75 dex. As a consequence, if a substantial fraction of galactic globular clusters has an external origin, they have to be mainly formed either in galaxies that are massive enough to ensure high levels of α-element abundances even at intermediate metallicity, or in lower mass dwarf galaxies accreted by the Milky Way in their early phases of formation. Finally, clusters in the metal-poor branch of the AMR present an anti-correlation of [SiCa/Fe] with the total cluster magnitude, while this is not the case for metal-rich branch clusters. In addition, this lack of faint high-α clusters in the young metal-poor population is in contrast with what is observed for old and more metal-poor clusters, possibly reflecting a higher heterogeneity of formation environments at lower metallicity. Accretion of high-mass satellites, as a major contribution to the current Milky Way globular cluster system both in the metal-poor and the metal-intermediate regime is compatible with the observations.