Methane hydrate (MH) is a non-stoichiometric inclusion compound encaging CH4 molecules in a framework of H-bonded water molecules. It has attracted considerable attention over the past decade both for its geophysical relevancy and for its possible energy and environmental applications. Pressure is a key parameter in the study of this system as it induces substantial variations in the size of the cages as well as complete structural rearrangements. However, up to date, only structural and vibrational studies have been carried on high pressure MH, while no information is available on the guest molecule self-dynamics in the different HP polymorphs. In a recent QENS experiment using the HP Paris-Edinburgh apparatus, we unexpectedly observed a clear diffusive dynamics of methane molecules during the sI-sII phase transition. This anomalous dynamics could be linked to the existence of a high-mobility disordered layer between sI and sII coexistence regions [1,2]. Here we propose to shed light on the origin of this motion by measuring the QENS signal of a much larger volume sample (0.5 cm3 of methane hydrate CH4:D2O) contained in a standard HP piston cylinder device, in the 1-5 kbar range.