Physical systems undergoing spontaneous pattern formation are governed by intrinsic length scales that may compete with extrinsic ones, resulting in exceptional spatiotemporal behaviour. In this work, we report experimental and theoretical evidence that spatial nonuniformity sets Faraday-wave patterns in motion, which are noticeable in the zigzag and drift dynamics exhibited by their wave crests. We provide a minimal theoretical model that succeeds in characterising the growth of localised patterns under nonuniform parametric driving. Furthermore, the derivation accounts for symmetry-breaking nonlinear gradients that we show are the source of the drift mechanism, which comes into play right after the system has crossed a secondary bifurcation point. Numerical solutions of the governing equations match our experimental findings and theoretical predictions. Our results advance the understanding of pattern behaviour induced by nonuniformity in generic nonlinear extended systems far from equilibrium.