  A complete, flux density limited sample of 96 faint ($> 0.5$ mJy) radio
sources is selected from the 10C survey at 15.7 GHz in the Lockman Hole. We
have matched this sample to a range of multi-wavelength catalogues, including
SERVS, SWIRE, UKIDSS and optical data; multi-wavelength counterparts are found
for 80 of the 96 sources and spectroscopic redshifts are available for 24
sources. Photometric reshifts are estimated for the sources with
multi-wavelength data available; the median redshift of the sample is 0.91 with
an interquartile range of 0.84. Radio-to-optical ratios show that at least 94
per cent of the sample are radio loud, indicating that the 10C sample is
dominated by radio galaxies. This is in contrast to samples selected at lower
frequencies, where radio-quiet AGN and starforming galaxies are present in
significant numbers at these flux density levels. All six radio-quiet sources
have rising radio spectra, suggesting that they are dominated by AGN emission.
These results confirm the conclusions of Paper I that the faint, flat-spectrum
sources which are found to dominate the 10C sample below $\sim 1$ mJy are the
cores of radio galaxies. The properties of the 10C sample are compared to the
SKADS Simulated Skies; a population of low-redshift starforming galaxies
predicted by the simulation is not found in the observed sample.
