In a comprehensive infrared study, the molecular vibrational features of (TMTTF)2SbF6, (TMTTF)2AsF6 and (TMTTF)2PF6 single crystals have been measured down to temperatures as low as 7 K by applying hydrostatic pressure up to 11 kbar. We follow the charge disproportionation below the critical temperatures T CO as pressure increases, and determine the critical pressure values p CO at which the charge-ordered phase is suppressed. The coexistence of the spin-Peierls phase with charge order is explored at low temperatures, and the competition of these two phases is observed. Based on our measurements we construct a generic phase diagram of the Fabre salts with centrosymmetric anions. The pressure-dependent anion and methyl-group dynamics in these quasi-one-dimensional charge transfer compounds yields information about the interplay of the organic molecules in the stacks and the anions, and how this interaction varies upon the transition to the charge-ordered state.