  We study the phase transition between conducting and insulating states taking
place in disordered multi-channel Luttinger liquids with inter-channel
interactions. We derive renormalisation group equations which are perturbative
in disorder but nonperturbative in interaction. In the vicinity of the
simultaneous phase transition in all channels, these equations become a set of
coupled Berezinskii--Kosterlitz--Thouless equations, which we analyze within
two models: an array of identical wires and a two-channel model with distinct
channels. We show that a competition between disorder and interaction results
in a variety of phases, expected to be observable at intermediate temperatures
where the interaction and disorder are relevant but weak hybridization and the
charge-density wave interaction may be ignored.
