We present high spatial resolution MERLIN 1.4GHz radio observations of two high redshift (z~2) sources, RGJ123623 (HDF147) and RGJ123617 (HDF130), selected as the brightest radio sources from a sample of submillimetre-faint radio galaxies. They have starburst classifications from their rest-frame UV spectra. However, their radio morphologies are remarkably compact (<80mas and <65mas respectively), demanding that the radio luminosity be dominated by Active Galactic Nuclei (AGN) rather than starbursts. Near-IR imaging (HST NICMOS F160W) shows large scale sizes (R_(1/2)~0.75, diameters ~12kpc) and SED fitting to photometric points (optical through the mid-IR) reveals massive (~5x10^(11) M_sun), old (a few Gyr) stellar populations. Both sources have low flux densities at observed 24um and are undetected in observed 70um and 850um, suggesting a low mass of interstellar dust. They are also formally undetected in the ultra-deep 2Ms Chandra data, suggesting that any AGN activity is likely intrinsically weak. We suggest both galaxies have evolved stellar populations, low star formation rates, and low accretion rates onto massive black holes (10^(8.6) M_sun) whose radio luminosity is weakly beamed (by factors of a few). A cluster-like environment has been identified near HDF130 by an over-density of galaxies at z=1.99, reinforcing the claim that clusters lead to more rapid evolution in galaxy populations. These observations suggest that high-resolution radio (MERLIN) can be a superb diagnostic tool of AGN in the diverse galaxy populations at z~2.