The electronic structure of graphene on Cu(111) and Cu(100) single crystals is investigated using low energy electron microscopy, low energy electron diffraction and angle resolved photoemission spectroscopy. On both substrates the graphene is rotationally disordered and interactions between the graphene and substrate lead to a shift in the Dirac crossing of $sim$ -0.3 eV and the opening of a $sim$ 250 meV gap. Exposure of the samples to air resulted in intercalation of oxygen under the graphene on Cu(100), which formed a ($sqrt{2} times 2sqrt{2}$)R45$^{rm o}$ superstructure. The effect of this intercalation on the graphene $pi$ bands is to increase the offset of the Dirac crossing ($sim$ -0.6 eV) and enlarge the gap ($sim$ 350 meV). No such effect is observed for the graphene on Cu(111) sample, with the surface state at $Gamma$ not showing the gap associated with a surface superstructure. The graphene film is found to protect the surface state from air exposure, with no change in the effective mass observed.
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