We study the effect of a spiral corrugation on the outer surface of a fully metal-coated scanning near-field optical microscopy (SNOM) probe using the finite element method. The introduction of a novel form of asymmetry, devoid of any preferential spatial direction and covering the whole angular range of the originally axisymmetric tip, allows attaining strong field localization for a linearly polarised mode with arbitrary orientation. Compared to previously proposed asymmetric structures which require linearly polarised excitation properly oriented with respect to the asymmetry, such a configuration enables significant simplification in mode injection. In fact, not only is the need for the delicate procedure to generate radially polarised beams overcome, but also the relative alignment between the linearly polarised beam and the tip modification is no longer critical.