We aim at studying the gamma-ray burst (GRB), GRB 081008, environment by analysing the spectra of its optical afterglow. Ultraviolet and Visual Echelle Spectrograph/Very Large Telescope (UVES/VLT) high-resolution spectroscopy of GRB 081008 was secured ∼5 h after the Swift-BAT trigger. Our data set also comprises three VLT/FORS2 nearly simultaneous spectra of the same source. The availability of nearly simultaneous high- and low-resolution spectra for a GRB afterglow is an extremely rare event. The GRB-damped Lyman α system at z= 1.9683 shows that the interstellar medium (ISM) of the host galaxy is constituted by at least three components which contribute to the line profiles. Component I is the redmost one, and is 20 and 78 km s−1 redward components II and III, respectively. We detect several ground state and excited absorption features in components I and II. These features have been used to compute the distances between the GRB and the absorbers. Component I is found to be 52 ± 6 pc away from the GRB, while component II presents few excited transitions and its distance is 200+60− 80 pc. Component III only features a few, low-ionization and saturated lines suggesting that it is even farther from the GRB. Component I represents the closest absorber ever detected near a GRB. This (relatively) low distance can possibly be a consequence of a dense GRB environment, which prevents the GRB prompt/afterglow emission to strongly affect the ISM up to higher distances. The hydrogen column density associated with GRB 081008 is log NH/cm−2= 21.11 ± 0.10, and the metallicity of the host galaxy is in the range of [X/H] =−1.29 to −0.52. In particular, we found [Fe/H] =−1.19 ± 0.11 and [Zn/H] =−0.52 ± 0.11 with respect to solar values. This discrepancy can be explained by the presence of dust in the GRB ISM, given the opposite refractory properties of iron and zinc. By deriving the depletion pattern for GRB 081008, we find the optical extinction in the visual band to be AV∼ 0.19 mag. The curve-of-growth analysis applied to the FORS2 spectra brings column densities consistent at the 3σ level to that evaluated from the UVES data using the line-fitting procedure. This reflects the low saturation of the detected GRB 081008 absorption features.