Measurements of inclusive and direct photon production at mid-rapidity in pp collisions at $\sqrt{s}=2.76$ and 8 TeV are presented by the ALICE experiment at the LHC. The results are reported in transverse momentum ranges of $0.4<~p_{T}<~10$ GeV/$c$ and $0.3<~p_{T}<~16$ GeV/$c$, respectively. Photons are detected with the electromagnetic calorimeter~(EMCal) and via reconstruction of e$^+$e$^-$ pairs from conversions in the ALICE detector material using the central tracking system. For the final measurement of the inclusive photon spectra the results are combined in the overlapping $p_{T}$ interval of both methods. Direct photon spectra, or their upper limits at 90% C.L. are extracted using the direct photon excess ratio $R_{\gamma}$, which quantifies the ratio of inclusive photons over decay photons generated with a decay-photon simulation. An additional hybrid method, combining photons reconstructed from conversions with those identified in the EMCal, is used for the combination of the direct photon excess ratio $R_{\gamma}$, as well as the extraction of direct photon spectra or their upper limits. While no significant signal of direct photons is seen over the full $p_{T}$ range, $R_{\gamma}$ for $p_{T}>7$ GeV/$c$ is at least one $\sigma$ above unity and consistent with expectations from next-to-leading order pQCD calculations.