We present 2D, integral field spectroscopy covering the rest-frame wavelengths of strong optical emission lines in nine submillimetre luminous galaxies (SMGs) at 2.0 < z < 2.7. The Gemini-North/Near-Infrared Integral Field Spectrograph (NIFS) and Very Large Telescope (VLT) Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI) imaging spectroscopy allow the mapping of the gas morphologies and dynamics within the sources, and we measure an average Hα velocity dispersion of 〈σ〉 = 220 ± 80 km s−1 and an average half-light radius of 〈r1/2〉 = 3.7 ± 0.8 kpc. The dynamical measure, 〈Vobs/2σ〉 = 0.9 ± 0.1, for the SMGs is higher than in more quiescent star-forming galaxies at the same redshift, highlighting a difference in the dynamics of the two populations. The far-infrared star formation rates (SFRs) of the SMGs, measured using Herschel-SPIRE† far-infrared photometry, are on average 370 ± 90 M⊙ yr−1, which is ∼2 times higher than the extinction-corrected SFRs of the more quiescent star-forming galaxies. Six of the SMGs in our sample show strong evidence for kinematically distinct multiple components with average velocity offsets of 200 ± 100 km s−1 and average projected spatial offsets of 8 ± 2 kpc, which we attribute to systems in the early stages of major mergers. Indeed, all SMGs are classified as mergers from a kinemetry analysis of the velocity and dispersion field asymmetry. We bring together our sample with the seven other SMGs with integral field unit observations to describe the ionized gas morphologies and kinematics in a sample of 16 SMGs. By comparing the velocity and spatial offsets of the SMG Hα components with subhalo offsets in the Millennium Simulation data base, we infer an average halo mass for SMGs in the range of 13 < log (M[h−1 M⊙]) < 14. Finally, we explore the relationship between the velocity dispersion and star formation intensity within the SMGs, finding that the gas motions are consistent with the Kennicutt–Schmidt law and a range of extinction corrections, although they might also be driven by the tidal torques from merging or even the star formation itself.