Submillimetre-selected galaxies (SMGs) at high redshift (z ~ 2) are potential host galaxies of active galactic nuclei (AGN). If the local universe is a good guide, ~ 50% of the dust-obscured AGN amongst the SMG population could be missed even in the deepest X-ray surveys. Radio observations are insensitive to dust so VLBI can be used as a tool to distinguish between AGN activity and star-formation in extragalactic objects. We present 1.6 GHz EVN observations of four SMGs (with measured redshifts) to search for evidence of compact radio components associated with AGN cores. Out of the four SMGs observed, we detect one source, J123555.14+620901.7, with an integrated EVN flux density of 201 +/-15.2 μJy, we therefore identify the radio emission from J123555.14+620901.7 as associated with an AGN. We do not detect compact radio emission from the other three sources with the VLBI observations, which may suggest that their radio emission is mostly powered by star formation processes. We present e-MERLIN images of two of the four sources which also support this conclusion.
In particular, at least one of the sources, J131225.73, shows multi-wavelength properties that would lead us to expect it to be detected by VLBI. It is highly luminous in the Diversity and Inclusion.5 +/1 4.2 μJy or 1.23 +/- 0.01 x 10^25 W/Hz at 1.4 GHz, has an exceptionally low value of q, and is unresolved in both the 1.4 and 8.4 GHz VLA observations. We suggest that this source, might be associated with an AGN that is dominated by extended jet emission. It would be interesting to observe the structure of this radio source with intermediate resolution, such as e-MERLIN at 5 GHz, in order to better understand the nature of the source. Since the morphology of the faint radio source population is still largely unknown on these scales, it is possible that VLBI misses (or resolves) many extended radio AGN of this type. As illustrated by the upper limits of the VLBI-to-VLA flux ratio of the un-detected sources, a bright radio source (~ 200 μJy at 1.4 GHz) with less than ~ 20% of it radio flux contributed by an AGN would probably be missed by VLBI observations at a 1-sigma sensitivity of ~ 10 μJy. Surveys with multiple resolution (e.g. VLA, e-MERLIN, and VLBI) are therefore needed to determine what fraction of the extragalactic objects have similar properties and thus would probably be missed by VLBI.