Determining criteria importance is a crucial task in multi-criteria decision-making problems, and the Best-Worst Method (BWM) has emerged as an effective weighting technique due to its reduced number of pairwise comparisons. Although BWM has been extended to handle group decision-making and linguistic information, existing approaches do not adequately address disagreements among evaluators, which may lead to dissatisfaction with the resulting criteria weights. To address this limitation, this paper proposes a consensus-based BWM for linguistic multi-criteria group decision-making. The proposed approach obtains consensual collective weights by minimally modifying the evaluators’ initial linguistic preferences. The resulting solution can support moderators and evaluators during consensus-reaching processes by facilitating the identification of disagreements and the generation of appropriate recommendations. The proposal is developed within the 2-tuple linguistic framework and provides both numerical and linguistic representations of the resulting weights. In addition, a novel stochastic consistency index is introduced to assess the reliability of evaluators’ preferences. The feasibility and effectiveness of the proposal are illustrated through a real-world case study and analysed by means of comparative and sensitivity analyses.