  We construct a Poisson algebra of brane currents from a QP-manifold (alias
symplectic $L_\infty$-algebroid), and show their Poisson brackets take a
universal geometric form. This generalises a result of Alekseev and Strobl on
string currents and generalised geometry to include branes with worldvolume
gauge fields, such as the D3 and M5. Our result yields a universal expression
for the 't Hooft anomaly that afflicts isometries in the presence of fluxes. We
determine the current algebra in terms of (exceptional) generalised geometry,
and show that the tensor hierarchy gives rise to a brane current hierarchy.
Exceptional complex structures produce pairs of anomaly-free current
subalgebras on the M5-brane worldvolume.
