<p>This study deals with efficient numerical schemes for solving singularly perturbed Volterra–Fredholm integro-differential equations. On the layer adapted Shishkin mesh, the numerical solution is calculated using the upwind finite difference scheme for the differential part and the quadrature rule for the integral parts. The method proves to be first-order convergent in the maximum norm. Then, using a post-processing technique we significantly enhance the accuracy from first-order to second order. Further, a hybrid scheme on the nonuniform mesh is also constructed and analyzed whose solution converges uniformly, independent of the perturbation parameter, and directly gives second order accuracy. The convergence analysis is carried out for all the schemes and the theoretical results are validated through some numerical tests. Finally, a comparison of the computational cost taken shows the efficiency of the proposed work.</p>