Galaxies with different morphological characteristics likely have different evolutionary histories, such that understanding the mechanisms that drive morphological change can provide valuable insights into the galaxy evolution process. These mechanisms largely correlate with local environment, ultimately leading to the well-known local morphology–density relation. To explore how the morphology–density relation is produced, we must look to earlier times, and trace the co-evolution of environment and morphology in an un-biased and self-consistent manner. Here we use new environmental metrics from the Deep Extragalactic VIsible Legacy Survey (DEVILS) to explore the spectroscopic morphology–density relation at intermediate redshift (0.3$<$z$<$0.5) and compare directly to the Galaxy And Mass Assembly Survey (GAMA) at 0$<$z$<$0.08. Importantly, both the galaxy morphologies and environmental metrics in DEVILS and GAMA are derived in a very similar manner, reducing any methodology biases. We see a clear evolution in morphological classes between DEVILS and GAMA, which is modulated by environment. These trends are consistent with a scenario where in all environments disc-dominated galaxies are transitioning to classical bulge + disc systems (potentially via minor mergers and/or secular evolution), and in high-density environments there is an increasing prevalence of visually selected elliptical galaxies (potentially via major mergers and/or disc fading), with the fraction of ellipticals increasing by $\sim$0.3 in the most dense regions over the last $\sim$7 Gyr, but remaining largely unchanged in low-density environments.