Tabular data is routinely released by national statistical agencies (NSA) to disseminate aggregated information from some particular microdata. Prior to publication, these tables have to be treated to preserve information without disclosing confidential details from specific respondents. This statistical disclosure control problem is of main interest for any NSA. Most protection techniques rely on the formulation of a large mathematical programming problem, whose solution is computationally expensive even for tables of moderate size. One of these techniques is controlled tabular adjustment (CTA). Although CTA is more efficient than other protection methods, the resulting mixed integer linear problems (MILP) are still challenging. In this work an approach based on block coordinate descent decomposition is designed and applied to large CTA instances. This approach is compared with CPLEX, a state-of-the-art MILP solver. Our results, from both synthetic and real tables with up to 200000 cells, show that the new procedure has a better practical behaviour than a general solver, providing better solutions within a specified time limit (which is required by NSAs in real-world).