Submillimetre galaxies (SMGs) are thought to play a significant role in the evolution of the cosmic star formation rate density, contributing as much as ∼20–30% at z ∼ 2–3. It has been hypothesised that these extreme star-forming systems are the progenitors of local early-type cluster galaxies. If true, this would imply that SMGs should reside in galaxy cluster progenitors at high redshift. Whilst there are well-known examples of SMGs residing in protoclusters, these systems were selected for follow-up because of their high galaxy or SMG density. To explore the environments of SMGs in an unbiased way we have undertaken a narrowband VLT/HAWK-I study of H-alpha and [OIII] emitters around three ALMA-identified and spectroscopically-confirmed SMGs at z ∼ 2.3 and z ∼ 3.3, which were selected with no prior knowledge of their environments. On average, these SMGs reside in environments which are ∼2–4x overdense compared to the field. Our results suggest that SMGs do tend to reside in protocluster-like environments, supporting the claim that they likely evolve into the passive early-type galaxies observed in local clusters.