We present the first results from our on-going Australia Telescope Compact Array survey of CO(1-0) in ALMA-identified submillimetre galaxies in the Extended Chandra Deep Field South. Strong detections of CO(1-0) emission from two submillimetre galaxies, ALESS 122.1 (z = 2.0232) and ALESS 67.1 (z = 2.1230), were obtained. We estimate gas masses of M_gas ~ 1.3 \times 10^{11} M_odot and M_gas ~ 1.0 \times 10^{11} M_⊙ for ALESS 122.1 and ALESS 67.1, respectively, adopting alpha_CO = 1.0. Dynamical mass estimates from the kinematics of the CO(1-0) line yields M_dyn (sin i)^2 = 2.1 +- 1.1 \times 10^{11} M_odot and (3.2 +- 0.9) \times 10^{11} M_⊙ for ALESS 122.1 and ALESS 67.1, respectively. This is consistent with the total baryonic mass estimates of these two systems. We examine star formation efficiency using the L_FIR versus L'_CO(1-0) relation for samples of local ULIRGs and LIRGs, and more distant star-forming galaxies, with CO(1-0) detections. We find some evidence of a shallower slope for ULIRGs and SMGs compared to less luminous systems, but a larger sample is required for definite conclusions. We determine gas-to-dust ratios of 170 +- 30 and 140 +- 30 for ALESS 122.1 and ALESS 67.1, respectively, showing ALESS 122.1 has an unusually large gas reservoir. By combining the 38.1 GHz continuum detection of ALESS 122.1 with 1.4 and 5.5 GHz data, we estimate that the free-free contribution to radio emission at 38.1 GHz is 34 +- 17 microJy, yielding a star formation rate (1400 +- 700 M_⊙ yr^{-1}) consistent with that from the infrared luminosity. ; Comment: 10 pages, 5 figures, accepted for publication in MNRAS