We present integral field spectroscopy observations, covering the [O iii] λλ4959, 5007 emission-line doublet of eight high-redshift (z = 1.4–3.4) ultraluminous infrared galaxies (ULIRGs) that host active galactic nucleus (AGN) activity, including known submillimetre luminous galaxies. The targets have moderate radio luminosities that are typical of high-redshift ULIRGs (L1.4 GHz = 1024–1025 W Hz−1) and therefore are not radio-loud AGNs. We decouple kinematic components due to the galaxy dynamics and mergers from those due to outflows. We find evidence in the four most luminous systems ( erg s−1) for the signatures of large-scale energetic outflows: extremely broad [O iii] emission (full width at half-maximum ≈ 700–1400 km s−1) across ≈4–15 kpc, with high velocity offsets from the systemic redshifts (up to ≈850 km s−1). The four less luminous systems have lower quality data displaying weaker evidence for spatially extended outflows. We estimate that these outflows are potentially depositing energy into their host galaxies at considerable rates (–1045 erg s−1); however, due to the lack of constraints on the density of the outflowing material and the structure of the outflow, these estimates should be taken as illustrative only. Based on the measured maximum velocities (vmax ≈ 400–1400 km s−1) the outflows observed are likely to unbind some fraction of the gas from their host galaxies, but are unlikely to completely remove gas from the galaxy haloes. By using a combination of energetic arguments and a comparison to ULIRGs without clear evidence for AGN activity, we show that the AGN activity could be the dominant power source for driving all of the observed outflows, although star formation may also play a significant role in some of the sources.