Observations show that the interstellar medium (ISM) contains sub-structure on scales less than 1 pc, detected in the form of spatial and temporal variations in column densities or optical depth. Despite the number of detections, the nature and ubiquity of the smallscale structure in the ISM is not yet fully understood. We use UV absorption data mainly from the Far Ultraviolet Spectroscopic Explorer (FUSE) and partly from the Space Telescope Imaging Spectrograph (STIS) of six Large Magellanic Cloud (LMC) stars (Sk -67 • 111, LH 54-425, Sk -67 • 107, Sk -67 • 106, Sk -67 • 104, and Sk -67 • 101) that are all located within 5 of each other, and analyse the physical properties of the Galactic disc gas in front of the LMC on sub-pc scales. We analyse absorption lines of a number of ions within the UV spectral range. Most importantly, interstellar molecular hydrogen, neutral oxygen, and fine-structure levels of neutral carbon have been used in order to study changes in the density and the physical properties of the Galactic disc gas over small angular scales. At an assumed distance of 1 kpc, the 5 separation between Sk -67 • 111 and Sk -67 • 101 implies a linear extent of 1.5 pc.We report on column densities of H 2 , C i, N i, O i, Al ii, Si ii, P ii, S iii, Ar i, and Fe ii in our six lines of sight, as well as C i*, C i**, Mg ii, Si iv, S ii, Mn ii, and Ni ii for four of them. While most species do not show any significant variation in their column densities, we find an enhancement of almost 2 dex for H 2 from Sk -67 • 111 to Sk -67 • 101, accompanied by only a small variation in the O i column density. Based on the formation-dissociation equilibrium, we trace these variations to the actual density variations in the molecular gas. On the smallest spatial scale of <0.08 pc, between Sk -67 • 107 and LH 54-425, we find a gas density variation of a factor of 1.8. The line of sight towards LH 54-425 does not follow the relatively smooth change seen from Sk -67 • 101 to Sk -67 • 111, suggesting that sub-structure might exist on a smaller spatial scale than the linear extent of our sight-lines. The results show that we sample a mix of both neutral and ionised gas in our six lines of sight. Towards Sk -67 • 101 to Sk -67 • 107, we derive the temperature T exc 70 K for the inner self-shielded part of the gas based on the rotational excitation levels of H 2 , and an average density of n H 60 cm −3 , typical of that for CNM. The gas towards LH 54-425 and Sk -67 • 111 shows different properties, and T exc 200 K. Our observations suggest that the detected H 2 in these six lines of sight (with the extent of <1.5 pc) is not necessarily physically connected, but that we are sampling molecular cloudlets with pathlengths <0.1−1.8 pc and possibly different densities.