We demonstrate that efficient adiabatic nanofocusing of plasmons can be achieved using a sharp metal wedge (thin tapered film) on a dielectric substrate. It is shown that the quasisymmetric (with respect to the charge distribution across the wedge) plasmon mode can experience infinite adiabatic slowing down with both its phase and group velocities reducing to zero as the plasmon propagates towards the tip of the wedge. Conditions for strong local field enhancement near the tip are determined and analyzed. In particular, it is demonstrated that the electric field in the plasmon experiences much stronger local enhancement than the magnetic field. Two distinct asymptotic regimes with the electric field amplitude approaching either zero or infinity at the tip of the wedge (tapered film) are described. The results are compared to adiabatic nanofocusing of plasmons by metallic V grooves and sharp metal wedges in a uniform dielectric.