We have modelled Atacama Large Millimetre/sub-millimetre Array (ALMA) long baseline imaging of the strong gravitational lens system H-ATLAS J090311.6+003906 (SDP.81). We have reconstructed the distribution of band 6 and 7 continuum emission in the z = 3.042 source and determined its kinematic properties by reconstructing CO(5–4) and CO(8–7) line emission in bands 4 and 6. The continuum imaging reveals a highly non-uniform distribution of dust with clumps on scales of ∼200 pc. In contrast, the CO line emission shows a relatively smooth, disc-like velocity field which is well fitted by a rotating disc model with an inclination angle of (40 ± 5)° and an asymptotic rotation velocity of 320 km s−1. The inferred dynamical mass within 1.5 kpc is (3.5 ± 0.5) × 1010 M⊙ which is comparable to the total molecular gas masses of (2.7 ± 0.5) × 1010 M⊙ and (3.5 ± 0.6) × 1010 M⊙ from the dust continuum emission and CO emission, respectively. Our new reconstruction of the lensed Hubble Space Telescope near-infrared emission shows two objects which appear to be interacting, with the rotating disc of gas and dust revealed by ALMA distinctly offset from the near-infrared emission. The clumpy nature of the dust and a low value of the Toomre parameter of Q ∼ 0.3 suggest that the disc is in a state of collapse. We estimate a star formation rate in the disc of 470 ± 80 M⊙ yr−1 with an efficiency ∼65 times greater than typical low-redshift galaxies. Our findings add to the growing body of evidence that the most infrared luminous, dust obscured galaxies in the high-redshift Universe represent a population of merger-induced starbursts.