White spirit might be a bit harsh. Get hold of some ethyl acetate if you can, this is (I think) the solvent in nail varnish and ought to remove it too.
Nail varnish remover might work, but with any method there is the risk of spreading the stain through the cloth fibres unless you stick them in a washing machine after loosening up the varnish.
White spirit may well get it out, but why not use nail varnish remover? With all these solvent based approachees, though, test the colour-fastness of the garment first on the back of a seam, or somewhere else that wont show.
also when applying the solvent, quickly apply an adsorbent tissue to the surface. This will remove the varnish from the cloth without spreading it tooo far.