Long-haul backbone communication networks provide internet services across a region or a country. The access to internet at smaller areas and the functioning of other critical infrastructures rely on the long-haul backbone high speed services and resilience. Hence, such networks are key for the decision-making of internet service managers and providers, as well as for the management and control of other critical infrastructures. This paper proposes a critical link analysis of the physical infrastructure of the UK internet backbone network from a dynamic, complex network approach. To this end, perturbation network analyses provide a natural framework to measure the network tolerance facing structural or topological modifications. Furthermore, there have been taken into account variations on data-traffic for the internet backbone that usually happen in a typical day. The novelty of the proposal is, then, twofold: proposing a weighted (traffic informed) Laplacian matrix to compute a perturbation centrality measure, and enhancing it by a time-dependent perturbation analysis to detect changes in link criticality within the network, coming from data traffic variation in a day. The results show which are the most critical links at every time of the day, being of main importance for protection, maintenance and mitigation plans for the UK internet backbone.