A correlated sampling technique has been implemented to estimate the impact of cross section modifications on the neutron transport and in Monte Carlo simulations in one single calculation. This implementation has been coupled to a Total Monte Carlo approach which consists in propagating nuclear data uncertainties with random cross section files. The TMC-CS (Total Monte Carlo with Correlated Sampling) approach offers an interesting speed-up of the associated computation time. This methodology is detailed in this paper, together with two application cases to validate and illustrate the gain provided by this technique: the highly enriched uranium/iron metal core reflected by a stainless-steel reflector HMI-001 benchmark, and the PETALE experimental programme in the CROCUS zero-power light water reactor.