Epithelial tissues maintain a robust architecture which is important for their barrier function, but they are also remodelled through the reorganization of cell-cell contacts. Tissue stability requires intercellular adhesion mediated by E-cadherin, in particular its trans-association in homophilic complexes supported by actin filaments through beta- and alpha-catenin. How alpha-catenin dynamic interactions between E-cadherin/beta-catenin and cortical actin control both stability and remodelling of adhesion is unclear. Here we focus on Drosophila homophilic E-cadherin complexes rather than total E-cadherin, including diffusing 'free' E-cadherin, because these complexes are a better proxy for adhesion. We find that E-cadherin complexes partition in very stable microdomains (that is, bona fide adhesive foci which are more stable than remodelling contacts). Furthermore, we find that stability and mobility of these microdomains depend on two actin populations: small, stable actin patches concentrate at homophilic E-cadherin clusters, whereas a rapidly turning over, contractile network constrains their lateral movement by a tethering mechanism. alpha-Catenin controls epithelial architecture mainly through regulation of the mobility of homophilic clusters and it is largely dispensable for their stability. Uncoupling stability and mobility of E-cadherin complexes suggests that stable epithelia may remodel through the regulated mobility of very stable adhesive foci.