Gas hydrates (GHs) in water close to freezing temperatures can be stabilised via the formation of ice layers. In a recent work [Bostrom et al., Astron. Astrophys., A54, 650, 2021], it was found that a surface region with partial gas dilution could be essential for obtaining nano- to micron-sized anomalously stabilizing ice layers. In this paper, it is demonstrated that the Casimir-Lifshitz free energy in multi-layer systems could induce thinner, but more stable, ice layers in cavities than those found for gas hydrates in a large reservoir of cold water. The thickness and stability of such ice layers in a pore filled with cold water could influence the leakage of gas molecules. Additional contributions, e.g. from salt-induced stresses, can also be of importance, and are briefly discussed.