Established mimicry theory predicts that Batesian mimics are selected to resemble their defended models, while models are selected to become dissimilar from their mimics. However, this theory has mainly considered individual selection acting on solitary organisms such as adult butterflies. Although Batesian mimicry of social insects is common, the few existing applications of kin selection theory to mimicry have emphasized relatedness among mimics rather than among models. Here, we present a signal detection model of Batesian mimicry in which the population of defended model prey is kin structured. Our analysis shows for most of parameter space that increased average dissimilarity from mimics has a twofold group-level cost for the model prey: it attracts more predators and these adopt more aggressive attack strategies. When mimetic resemblance and local relatedness are sufficiently high, such costs acting in the local neighbourhood may outweigh the individual benefits of dissimilarity, causing kin selection to drive the models to resemble their mimics. This requires model prey to be more common than mimics and/or well-defended, the conditions under which Batesian mimicry is thought most successful. Local relatedness makes defended prey easier targets for Batesian mimicry and is likely to stabilize the mimetic relationship over time.