  We present a realisation of the universal/simple Bershadsky--Polyakov vertex
algebras as subalgebras of the tensor product of the universal/simple
Zamolodchikov vertex algebras and an isotropic lattice vertex algebra. This
generalises the realisation of the universal/simple affine vertex algebras
associated to $\mathfrak{sl}_2$ and $\mathfrak{osp}(1|2)$ given in
arXiv:1711.11342. Relaxed highest-weight modules are likewise constructed,
conditions for their irreducibility are established, and their characters are
explicitly computed, generalising the character formulae of arXiv:1803.01989.
