We report the results of a pilot study with the Expanded Very Large Array (EVLA) of 12CO J= 1–0 emission from four submillimetre-selected galaxies at z= 2.2–2.5, each with an existing detection of 12CO J= 3–2, one of which comprises two distinct spatial components. Using the EVLA’s most compact configuration, we detect strong, broad [medians: 990 km s−1 full width at zero intensity; 540 km s−1 full width at half-maximum (FWHM)]J= 1–0 line emission from all of our targets – coincident in position and velocity with their J= 3–2 emission. The median linewidth ratio, σ1–0/σ3–2= 1.15 ± 0.06, suggests that the J= 1–0 is more spatially extended than the J= 3–2 emission, a situation confirmed by our maps which reveal velocity structure in several cases and typical sizes of ∼16 kpc FWHM. The median brightness temperature (Tb) ratio is r3-2/1-0= 0.55 ± 0.05, consistent with local galaxies with LIR > 1011 L⊙, noting that our value may be biased high because of the J= 3–2 based sample selection. Naively, this suggests gas masses roughly two times higher than estimates made using higher J transitions of CO, with the discrepancy due entirely to the difference in assumed Tb ratio. We also estimate molecular gas masses using the 12CO J= 1–0 line and the observed global Tb ratios, assuming standard underlying Tb ratios for the non-star-forming and star-forming gas phases as well as a limiting star formation efficiency for the latter in all systems, i.e. without calling upon XCO (≡α). Using this new method, we find a median molecular gas mass of (2.5 ± 0.8) × 1010 M⊙, with a plausible range stretching up to three times higher. Even larger masses cannot be ruled out, but are not favoured by dynamical constraints: the median dynamical mass within R∼ 7 kpc for our sample is (2.3 ± 1.4) × 1011 M⊙ or ∼6 times more massive than UV-selected galaxies at this epoch. We examine the Schmidt–Kennicutt (S–K) relation for all the distant galaxy populations for which CO J= 1–0 or J= 2–1 data are available, finding small systematic differences between galaxy populations. These have previously been interpreted as evidence for different modes of star formation, but we argue that these differences are to be expected, given the still considerable uncertainties, certainly when considering the probable excitation biases due to the molecular lines used, and the possibility of sustained S–K offsets during the evolution of individual gas-rich systems. Finally, we discuss the morass of degeneracies surrounding molecular gas mass estimates, the possibilities for breaking them, and the future prospects for imaging and studying cold, quiescent molecular gas at high redshifts.