The impact of resonant magnetic perturbations (RMPs) on the power required to access H-mode is examined experimentally on MAST. Applying RMP in n = 2, 3, 4 and 6 configurations delays the L-H transition at low applied fields and prevents the transition at high fields. The experiment was primarily performed at RMP fields sufficient to cause moderate increases in ELM frequency, f mitigated/ f natural ~ 3. To obtain H-mode with RMPs at this field, an increase of injected beam power is required of at least 50% for n = 3 and n = 4 RMP and 100% for n = 6 RMP. In terms of power threshold, this corresponds to increases of at least 20% for n = 3 and n = 4 RMPs and 60% for n = 6 RMPs. This 'RMP affected' power threshold is found to increase with RMP magnitude above a certain minimum perturbed field, below which there is no impact on the power threshold. Extrapolations from these results indicate large increases in the L-H power threshold may be required for discharges requiring large mitigated ELM frequency.