Homophilic interactions between E-Cadherin molecules generate adhesive interfaces or junctions (AJs) that connect neighbouring cells in epithelial monolayers. These are highly dynamic structures. Under conditions of homeostasis, changes in the length of individual interfaces provide epithelia with the fluidity required to maintain tissue integrity in the face of cell division, delamination and extrinsic forces. Furthermore, when acted upon by polarized actomyosin-based forces, changes in AJ length can also drive neighbour exchange to reshape an entire tissue. Whilst the contribution of AJ remodelling to developmental morphogenesis has been subjected to intensive study, less is known about AJ dynamics in other circumstances. Here, using a combination of experiment and computational modelling, we study AJ dynamics in an epithelium that undergoes a gradual increase in packing order without concomitant large-scale changes in tissue shape or size. Under these conditions, we find that neighbour exchange events are driven by stochastic fluctuations in junction length, which are regulated at least in part by the level of junctional actomyosin. As a result of this behaviour, the steady increase in junctional actomyosin and consequent tension that accompanies development steadily reduces the rate of neighbour exchange and orders the tissue. This leads us to propose a model in which topological transitions, that underpin tissue fluidity, are either inhibited or biased by actomyosin-based forces, to drive, respectively, tissue ordering or deformation.