Abstract We studied the symmetry of magnetic properties and the resulting magnetic textures in ultra-thin epitaxial Au_0.67Pt_0.33/Co/W(110), a model system exhibiting perpendicular magnetic anisotropy and interface Dzyaloshinskii–Moriya interaction (DMI). As a peculiar feature, the C_2v crystal symmetry induced by the Co/W interface results in an additional uniaxial in-plane magnetic anisotropy in the cobalt layer. Photo-emission electron microscopy with magnetic sensitivity reveals the formation of self-organised magnetic stripe domains oriented parallel to the hard in-plane magnetisation axis. We attribute this behavior to the lower domain wall energy when oriented along this axis, where both the DMI and the in-plane magnetic anisotropy favor a Néel domain wall configuration. The anisotropic domain wall energy also leads to the formation of elliptical skyrmion bubbles under a weak out-of-plane magnetic field.