Megahertz peaked-spectrum (MPS) sources have spectra that peak at frequencies below 1 GHz in the observer's frame and are believed to be radio-loud active galactic nuclei (AGN). We recently presented a new method to search for high-redshift AGN by identifying unusually compact MPS sources. In this paper, we present European VLBI Network (EVN) observations of 11 MPS sources which we use to determine their sizes and investigate the nature of the sources with ~10 mas resolution. Of the 11 sources, we detect 9 with the EVN. Combining the EVN observations with spectral and redshift information, we show that the detected sources are all AGN with linear sizes smaller than 1.1 kpc and are likely young. This shows that low-frequency colour-colour diagrams are an easy and efficient way of selecting small AGN and explains our high detection fraction (82 per cent) in comparison to comparable surveys. Finally we argue that the detected sources are all likely compact symmetric objects and that none of the sources are blazars.