We study the impact of active galactic nuclei (AGN) ionised outflows on star formation in high-redshift AGN host galaxies, by combining near-infrared integral field spectroscopic (IFS) observations, mapping the H emission and [O iii]5007 outflows, with matched-resolution observations of the rest-frame far-infrared (FIR) emission.We present high-resolution ALMA Band 7 observations of eight X-ray selected AGN (L2-10 keV = 1043:81045:2 erg s1) at z 2 from the SUPER (SINFONI Survey for Unveiling the Physics and Eect of Radiative feedback) sample, targeting the observed-frame 870 m (rest-frame 260 m) continuum at 2 kpc (0.200) spatial resolution. The targets were selected among the SUPER AGN with an [O iii] detection in the IFS maps and with a detection in the FIR photometry. We detected six out of eight targets with signal-to-noise ratio S=N & 10 in the ALMA maps, from which we measured continuum flux densities in the range 0:272:58 mJy and FIR half-light radii (Re) in the range 0:8-2:1 kpc. The other two targets were detected with S/N of 3.6 and 5.9, which are insucient for spatially resolved analysis. The FIR Re of our sample are comparable to other AGN and star-forming galaxies at a similar redshift from the literature. However, combining our sample with the literature samples, we find that the mean FIR size in X-ray AGN (Re = 1:16 0:11 kpc) is slightly smaller than in non-AGN (Re = 1:69 0:13 kpc). From spectral energy distribution fitting, we find that the main contribution to the 260 m flux density is dust heated by star formation, with 4% contribution from AGN-heated dust and 1% from synchrotron emission. The majority of our sample show dierent morphologies for the FIR (mostly due to reprocessed stellar emission) and the ionised gas emission (H and [O iii], mostly due to AGN emission). This could be due to the dierent locations of dust and ionised gas, the dierent sources of the emission (stars and AGN), or the eect of dust obscuration.We are unable to identify any residual H emission, above that dominated by AGN, that could be attributed to star formation. Under the assumption that the FIR emission is a reliable tracer of obscured star formation, we find that the obscured star formation activity in these AGN host galaxies is not clearly aected by the ionised outflows. However, we cannot rule out that star formation suppression is happening on smaller spatial scales than the ones we probe with our observations (<2 kpc) or on dierent timescales.