The environment of supernova remnants (SNRs) is a key factor in their evolution, particularly at later stages of their existence. Mixed-morphology (MM) SNRs have a peculiar centre-filled X-ray shape that remains enigmatic. It is often assumed that they evolve in very dense environments, and that the X-ray morphology is due to interactions between the SNRs and their surroundings. We aim to determine whether VRO 42.05.01 is embedded in, and interacting with, a dense molecular environment. We also aim to understand the multi-wavelength emission from the environment of this SNR, and whether the interstellar material can be responsible for the the MM nature of the source, and for its strange radio and optical shape. We used the IRAM telescope in Pico Veleta, Spain, to search for signs of interaction between the SNR and neighbouring molecular clouds. We observed a region of 260 140 towards the west of VRO 42.05.01 and a region of 80 40 towards the north of the remnant in the ^12^CO J=1-0, ^13^CO J=1-0, and ^12^CO J=2-1 transitions with the EMIR receiver. We made maps of the properties of the observed molecular clouds (peak temperatures, central velocities, velocity dispersions), as well as maps of column density along the line of sight, and ratio of the ^12^CO J=2-1 to ^12^CO J=1-0 transitions.We also analyse archival optical, infrared, and radio spectroscopic data for other hints on the nature of the medium. We do not find conclusive physical proof that the SNR is interacting with the few, clumpy molecular clouds that surround it in the region of our observations, although there is some suggestion of such interaction (in a region outside our map) from infrared emission. We find that there is a velocity gradient in one of the molecular clouds that is consistent with a stellar wind blown by a 12-14M_{sun}_ progenitor star.We reassess the literature distance to VRO 42.05.01, and propose that it has a local standard of rest velocity of ~6km/s, and that it is located 1.0+/-0.4kpc away (the earlier distance value was 4.5+/-1.5kpc).We find that a dust sheet intersects VRO 42.05.01 and is possibly related to its double shell-shaped morphology.