The presence of a chain of magnetic islands, produced by externally applied tri-dimensional fields at a rational surface, is numerically found to have significant effects on the resonant response, as well as on the associated toroidal torques, in a toroidal tokamak plasma with conventional aspect ratio, strong shaping, and in the regime of slow toroidal flow. With an ad hoc assumption of the local flattening of the equilibrium pressure profile by the islands, it is found that the primary effect is the increasing of the resonant response by islands, at slow flow, due to the reduction of the favourable average curvature effect. This also leads to the reduction of the toroidal torques, in particular that associated with the neoclassical toroidal viscosity. Partial or complete flattening of the local pressure profile, depending on the island size, results in partial or full recovering of the so called constant-ψ plasma response regime. Computational results are well fitted by analytic models for the two extreme cases: the case of complete flattening and the case of no flattening of the local pressure.