We present millimetre observations of a sample of 12 high-redshift ultraluminous infrared galaxies (ULIRGs) in the extended growth strip (EGS). These objects were initially selected on the basis of their observed mid-IR colours (0.0 < 3.6−4.5 < 0.4 and −0.7 < 3.6−8.0 < 0.5) to lie at high redshift 1.5 ≲z≲ 3, and subsequent 20–38 μm mid-IR spectroscopy confirms that they lie in a narrow redshift window centred on z≈ 2. We detect 9/12 of the objects in our sample at high significance (>3σ) with a mean 1200 μm flux of 〈F1200 μm〉= 1.6 ± 0.1 mJy. Our millimetre photometry, combined with existing far-IR photometry from the Far-IR Deep Extragalactic Legacy Survey (FIDELS) and accurate spectroscopic redshifts, places constraints both sides of the thermal dust peak. This allows us to estimate the dust properties, including the far-IR luminosity, dust temperature and dust mass. We find that our sample is similar to other high-z and intermediate-z ULIRGs, and local systems, but has a different dust selection function than submillimeter-selected galaxies. Finally, we use existing 20-cm radio continuum imaging to test the far-IR/radio correlation at high redshift. We find that our sample is consistent with the local relation, implying little evolution. Furthermore, this suggests that our sample selection method is efficient at identifying ultraluminous, starburst-dominated systems within a very narrow redshift range centred at z∼ 2.