We demonstrate that the propagation velocity of field driven magnetic domain walls in ultrathin Au/Co/Au films with perpendicular anisotropy on vicinal substrates is anisotropic and strongly depends on the step density of the substrate. The velocity of walls oriented perpendicular to the steps drastically increases with increasing local step density while being unchanged or only weakly decreased for the walls oriented parallel to the steps. We develop an analytical model revealing the step-modified exchange interactions as the main driving force for this anisotropic behavior. The enhancement of the domain wall velocity at low magnetic fields far below the Walker instability threshold makes this phenomenon interesting for magnetic nanodevices.