We research the requirements of high contrast imaging when combined with the cross-correlation (CC) of high-resolution spectra with known spectroscopic templates for detecting and characterizing exoplanets in reflected light. We simulate applying the technique to a potentially habitable Proxima b-like planet and show that the O2 A-band spectral feature could feasibly be detected on nearby rocky exoplanets using future instruments on the ELT. The technique is then more widely analysed showing that detections of planets and O2 with signal-to-noise ratio in the CC function (SNRCC) >3 can be obtained when the signal-to-noise ratio of the simulated planet spectrum (SNRspec) is from 0.25 to 1.2. We place constraints on the spectral resolution, instrument contrast, point spread function (PSF), exposure times and systematic error in stellar light subtraction for making such detections. We find that accurate stellar light subtraction (with 99.99 per cent removal) and PSFs with high spatial resolutions are key to making detections. Lastly a further investigation suggests the ELT could potentially discover and characterize planets of all sizes around different spectral type stars, as well as detecting O2 on super-Earths with habitable zone orbits around nearby M stars.GAH acknowledges the support of an STFC PhD Studentship in writing the manuscript
