  We obtain a bound on the expectation of the spectral shift function for
alloy-type random Schr\"odinger operators on $\mathbb{R}^d$ in the region of
localisation, corresponding to a change from Dirichlet to Neumann boundary
conditions along the boundary of a finite volume. The bound scales with the
area of the surface where the boundary conditions are changed. As an
application of our bound on the spectral shift function, we prove a reverse
Wegner inequality for finite-volume Schr\"odinger operators in the region of
localisation with a constant locally uniform in the energy. The application
requires that the single-site distribution of the independent and identically
distributed random variables has a Lebesgue density that is also bounded away
from zero. The reverse Wegner inequality implies a strictly positive, locally
uniform lower bound on the density of states for these continuum random
Schr\"odinger operators.
