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Nuclear magnetic resonance (NMR) investigations of methyl tunnelling in acetophenone in the solid state are reported. Measurements of the proton spin-lattice relaxation time and of the methyl tunnelling frequency ( nu t=1.435 MHz) from dipole-dipole-driven low-field NMR demonstrate that the methyl group in acetophenone has an anomalously high potential barrier. A comparison with similar measurements on trans-4-phenyl-3-buten-2-one, along with a theoretical calculation of the respective barrier contributions, leads the authors to conclude that the origin of the barrier lies predominantly in the interaction between hydrogen atoms on the methyl and phenyl groups. The tunnelling sideband measurements reported extend the window of low-field NMR into the megahertz region and illustrate the existence of a NMR sideband intensity enhancement when the system is close to the level crossing between Zeeman states of the E and A manifolds, respectively.