We investigate the environment of 23 submillimetre galaxies (SMGs) drawn from a signal-to-noise (S/N)-limited sample of SMGs originally discovered in the James Clerk Maxwell Telescope (JCMT)/AzTEC 1.1 mm continuum survey of a Cosmic Evolution Survey (COSMOS) subfield and then followed up with the Submillimetre Array and Plateau de Bure Interferometer at 890 μm and 1.3 mm, respectively. These SMGs already have well- defined multiwavelength counterparts and redshifts. We also analyse the environments of four COSMOS SMGs spectroscopically confirmed to lie at redshifts z_(spec) > 4.5, and one at z_(spec) = 2.49 resulting in a total SMG sample size of 28. We search for overdensities using the COSMOS photometric redshifts based on over 30 UV- NIR photometric measurements including the new UltraVISTA data release 2 and Spitzer/SPLASH data, and reaching an accuracy of σ_(Δz/ (1 + z)) = 0.0067 (0.0155) at z < 3.5 (>3.5). To identify overdensities we apply the Voronoi tessellation analysis, and estimate the redshift-space overdensity estimator δ_g as a function of distance from the SMG and/or overdensity centre. We test and validate our approach via simulations, X-ray detected groups or clusters, and spectroscopic verifications using VUDS and zCOSMOS catalogues which show that even with photometric redshifts in the COSMOS field we can efficiently retrieve overdensities out to z ≈ 5. Our results yield that 11 out of 23 (48%) JCMT/AzTEC 1.1 mm SMGs occupy overdense environments. Considering the entire JCMT/AzTEC 1.1 mm S/N ≥ 4 sample and taking the expected fraction of spurious detections into account, this means that 35–61% of the SMGs in the S/N- limited sample occupy overdense environments. We perform an X-ray stacking analysis in the 0.5–2 keV band using a 32″ aperture and our SMG positions, and find statistically significant detections. For our z < 2 subsample we find an average flux of (4.0 ± 0.8) × 10^(-16) erg s^(-1) cm^(-2) and a corresponding total mass of M_(200) = 2.8 × 10^(13)M⊙. The z > 2 subsample yields an average flux of (1.3 ± 0.5) × 10^(-16) erg s^(-1) cm^(-2) and a corresponding total massof M_(200) = 2 × 10^(13)M⊙. Our results suggest a higher occurrence of SMGs occupying overdense environments at z ≥ 3 than at z < 3. This may be understood if highly star-forming galaxies can only be formed in the highest peaks of the density field tracing the most massive dark matter haloes at early cosmic epochs, while at later times cosmic structure may have matured sufficiently that more modest overdensities correspond to sufficiently massive haloes to form SMGs.