Bandgap engineering in lead-free Cs2Ag1-xNaxBiCl6 (x = 0 to 1) double perovskite alloys synthesized through solution-based approach is investigated. The bandgap is shown to vary from 2.64 eV to 3.01 eV as Ag+ at B′ site gets replaced with Na+ cation. Despite a linear change in the lattice parameter according to Vegard's law, bandgap (Eg) changes in a nonlinear fashion for x = 0 to 1 with much lower Eg values observed than predicted by Vegard's rule. Further, we show the bandgap bowing effect in Cs2Ag1-xNaxBiCl6. Raman spectroscopic studies reveal that the changes in the vibrational mode positions arise due to the systematic variations in local distortions of [BiCl6]3- and [AgCl6]5- octahedra. The bandgap change, Raman mode frequency shift, Raman peak width, and the ratio of intensities of Raman modes all show a similar trend as a function of Na substitution concentration (x). The changes are minimal and linear for x from 0 to ∼0.6 and deviate sharply for higher Na concentration (x > 0.6). These observations strongly suggest that the sublattice distortion in the A2B′B″X6 lattice arises due to a mismatch in the octahedra. This imparts a nonlinear change in the bandgap. Thus, a strong interplay between the [Ag(Na)Cl6]5- and [BiCl6]3- octahedra is shown to have a significant influence on the deviation of bandgap from Vegard's rule and further enforces the bandgap bowing effect in Cs2Ag1-xNaxBiCl6. © 2021 Author(s).