We study a large sample of ~4000 Lyα Emitters (LAEs) and identify the active galactic nuclei (AGN) among them in order to characterise their evolution across cosmic time. This work was carried out using the SC4K survey (Sobral et al. 2018) and data collected by the Hubble Space Telescope (HST), Chandra X-ray Observatory and the Very Large Array (VLA). We find 322 X-ray or radio detected AGN within the sample, constituting 8.7±0.5% of the sources considered. We find that the vast majority of classifiable AGN (81±3%) are point-like or compact sources in the rest-frame UV seen with HST, and this qualitative trend holds regardless of detection band or redshift. These AGN have a range of black hole accretion rates (BHARs), and we present the first direct comparison between radio and X-ray BHARs. X-ray calculated BHARs range from ~0.07 M⊙/yr to ~23 M⊙/yr, indicating a highly varied sample, with some very active AGN detected. Radio calculated BHARs range from ~0.09 M⊙/yr to ~8.8 M⊙/yr, broadly tracing the same range as the X-ray calculated BHARs. X-ray calculated BHARs peak at z~3 and both radio and X-ray calculated BHARs increase with increasing redshift, plateauing at z~4. We find significantly less variation in radio BHARs when compared to X-ray BHARs, indicating radio may be a far more stable and reliable method of calculating the BHARs of AGN over large timescales, while X-ray is more suitable for instantaneous BHARs.