We present an accurate analysis of the H2 absorption lines from the z abs ∼ 2.4018 damped Lyα system towards HE 0027−1836 observed with the Very Large Telescope Ultraviolet and Visual Echelle Spectrograph (VLT/UVES) as a part of the European Southern Observatory Large Programme 'The UVES large programme for testing fundamental physics' to constrain the variation of proton-to-electron mass ratio, μ ≡ m p /m e . We perform cross-correlation analysis between 19 individual exposures taken over three years and the combined spectrum to check the wavelength calibration stability. We notice the presence of a possible wavelength-dependent velocity drift especially in the data taken in 2012. We use available asteroids spectra taken with UVES close to our observations to confirm and quantify this effect. We consider single- and two-component Voigt profiles to model the observed H2 absorption profiles. We use both linear regression analysis and Voigt profile fitting where Δμ/μ is explicitly considered as an additional fitting parameter. The two-component model is marginally favoured by the statistical indicators and we get Δμ/μ = −2.5 ± 8.1stat ± 6.2sys ppm. When we apply the correction to the wavelength-dependent velocity drift, we find Δμ/μ = −7.6 ± 8.1stat ± 6.3sys ppm. It will be important to check the extent to which the velocity drift we notice in this study is present in UVES data used for previous Δμ/μ measurements.