The classic model of eukaryotic gene expression requires direct spatial contact between a distal enhancer and a proximal promoter. However, recent chromosome conformation capture studies (e.g. Hi-C) show that enhancer and promoters are embedded in a complex network of cell-type specific looping interactions. Here we investigate whether, and to what extent, looping interactions between elements in the vicinity of an enhancer-promoter pair can influence the frequency of enhancer-promoter contacts. Our polymer simulations show that a chromatin loop formed by elements flanking either an enhancer or a promoter suppresses enhancer-promoter interactions, working as a topological insulator. A loop formed by elements located in the region between an enhancer and a promoter, on the contrary, facilitates their interactions. We find that these two consequences of chromatin loops have different genomic extents, with facilitation being a local effect and insulation persisting over a large range of genomic distances. Overall, our results show that looping interactions which do not directly involve an enhancer-promoter contact can nevertheless significantly modulate their interactions. This illustrates the intricate effects that local chromatin organization can have on gene expression.