We present an analysis of the spatial clustering of a large sample of high-resolution, interferometically identified, submillimetre galaxies (SMGs). We measure the projected cross-correlation function of ∼350 SMGs in the UKIDSS Ultra Deep-Survey Field across a redshift range of z = 1.5-3 utilizing a method that incorporates the uncertainties in the redshift measurements for both the SMGs and cross-correlated galaxies through sampling their full probability distribution functions. By measuring the absolute linear bias of the SMGs, we derive halo masses of log 10 (M_ halo[h-1, M⊙]) ∼12.8 with no evidence of evolution in the halo masses with redshift, contrary to some previous work. From considering models of halo mass growth rates, we predict that the SMGs will reside in haloes of mass log 10(M halo[{h-1,\rm M⊙]) ∼13.2 at z = 0, consistent with the expectation that the majority of z = 1.5-3 SMGs will evolve into present-day spheroidal galaxies. Finally, comparing to models of stellar-to-halo mass ratios, we show that SMGs may correspond to systems that are maximally efficient at converting their gas reservoirs into stars. We compare them to a simple model for gas cooling in haloes that suggests that the unique properties of the SMG population, including their high levels of star formation and their redshift distribution, are a result of the SMGs being the most massive galaxies that are still able to accrete cool gas from their surrounding intragalactic medium.