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The influence of structural disorder on the thermal transport in the colusite $\mathrm{C}{\mathrm{u}}_{26}{\mathrm{V}}_{2}\mathrm{S}{\mathrm{n}}_{6}{\mathrm{S}}_{32}$ has been investigated by means of low-temperature thermal conductivity and specific heat measurements (2--300 K), $^{119}\mathrm{Sn}$ M\"ossbauer spectroscopy and temperature-dependent powder inelastic neutron scattering (INS). Variations in the high-temperature synthesis conditions act as a key parameter for tuning the degree of disorder in colusite compounds. Intriguingly, we find that all synthesized samples are disordered, the degree of which varies with the synthesis conditions used. M\"ossbauer data clearly evidence that Sn atoms do not solely occupy the $6c$ site of the crystal lattice but are present on possibly both the Cu and V sites, leading to a random distribution of these three cations within the unit cell. Increasing the disorder in these materials tends to lead to a smearing out of the main features in the phonon density of states measured by INS. Although the evolution of the inelastic signal upon warming is well described by a quasiharmonic approximation, elastic properties calculations indicate large average Gr\"uneisen parameters, consistent with those determined experimentally from thermodynamic data. Increasing the level of disorder results in a decreased average Gr\"uneisen parameter suggesting that the lowered lattice thermal conductivity is not driven by enhanced anharmonicity. These results provide experimental evidence to support that the remarkable changeover in the lattice thermal conductivity from crystalline to glasslike is solely driven by enhanced disorder accompanied by local lattice distortions.