A novel finite volume method, described in Part I of this paper (Sabin and Owens, Int. J. Numer. Meth. Fluids 2003; 42:57-77), is applied in the linear stability analysis of a lid-driven cavity flow in a square enclosure. A combination of Amoldi's method and extrapolation to zero mesh size allows us to determine the first critical Reynolds number at which Hopf bifurcation takes place. The extreme sensitivity of the predicted critical Reynolds number to the accuracy of the method and to the treatment of the singularity points is noted. Results are compared with those in the literature and are in very good agreement. Copyright (C) 2003 John Wiley Sons, Ltd.