  We use Gaia-ESO Survey iDR4 data to explore the Mg-Al anti-correlation in
globular clusters, that were observed as calibrators, as a demonstration of the
quality of Gaia-ESO Survey data and analysis. The results compare well with the
available literature, within 0.1 dex or less, after a small (compared to the
internal spreads) offset between the UVES and the GIRAFFE data of 0.10-0.15 dex
was taken into account. In particular, we present for the first time data for
NGC 5927, one of the most metal-rich globular clusters studied in the
literature so far with [Fe/H]=-0.49 dex, that was included to connect with the
open cluster regime in the Gaia-ESO Survey internal calibration. The extent and
shape of the Mg-Al anti-correlation provide strong constraints on the multiple
population phenomenon in globular clusters. In particular, we studied the
dependency of the Mg-Al anti-correlation extension with metallicity,
present-day mass, and age of the clusters, using GES data in combination with a
large set of homogenized literature measurements. We find a dependency with
both metallicity and mass, that is evident when fitting for the two parameters
simultaneously, but no significant dependency with age. We confirm that the
Mg-Al anti-correlation is not seen in all clusters, but disappears for the less
massive or most metal-rich ones. We also use our dataset to see whether a
normal anti-correlation would explain the low [Mg/$\alpha$] observed in some
extragalactic globular clusters, but find that none of the clusters in our
sample can reproduce it, and more extreme chemical compositions (like the one
of NGC 2419) would be required. We conclude that GES iDR4 data already meet the
requirements set by the main survey goals, and can be used to study in detail
globular clusters even if the analysis procedures were not specifically
designed for them.
