  We present a lattice analysis of the light pseudoscalar mesons with
consideration for the mixing between the flavour-neutral states $\pi^0$, $\eta$
and $\eta^\prime$. We extract the masses and flavour compositions of the
pseudoscalar meson nonet in $n_f=1+1+1$ lattice QCD+QED around an SU(3)-flavour
symmetric point, and observe flavour-symmetry features of the extracted data,
along with preliminary extrapolation results for the flavour compositions at
the physical point. A key result of this work is the observed mass splitting
between the $\pi^0$ and $\eta$ on our ensembles, which is found to exhibit
behaviour that is simply related to the corresponding flavour compositions.
