We study a generic model for the polarisation and motility of cells and biomimetic systems interacting with a viscous substrate, where traction forces generated by the cell are modelled by means of oscillating force multipoles at the cell/substrate interface. We find that symmetry breaking and cell polarisation naturally “emerge” from long-range mechanical interactions between oscillating units, mediated both by the intracellular medium and the substrate. However, the harnessing of cell polarisation for motility requires substrate-mediated interactions.Motility can be optimised by adapting the oscillation frequency to the relaxation time of the system, and maximal velocity is found when the substrate and cell viscosities match. Cellular noise can destroy mechanical coordination between force-generating elements within the cell, resulting in sudden changes of polarisation. The persistence of the cell's motion is found to depend on the substrate viscosity. Within such a model, chemotactic guidance of cell motion is obtained by directionally modulating the persistence of motion, rather than by modulating cell motility, in a way that resemble the run and tumble chemotaxis of bacteria.