A model of the diffusion of a tagged particle moving by hopping on a lattice, where a finite concentration c of background particles gives rise to blocking due to forbidden multiple occupancy of sites, is extended to the situation where disorder exists on the lattice. In this paper the specific case of variable bond hopping rates is considered in the strongly disordered limit where a finite concentration p of the bonds are completely blocked. The resulting self-diffusion coefficient takes the form (1 - c)(1 - p/p(c))D(0)f where p(c) is the percolation limit and f is the dynamical correlation factor. It is expected that f is affected by the disorder and this is estimated by random-walk theory through a calculation of (cos theta) where theta is the angle between successive jumps of a particle and a vacancy. Also a quite comprehensive simulation study of tracer diffusion in a two-dimensional square lattice for 0 < c < 1 and 0 < p < p(c) is performed. The results are in good agreement with the analytical results which are known for small concentrations. Our approximate theory gives a good description over the entire range provided that the corrected form of (cos theta) is used.