Abstract. Development of fundamental physics relies on the constancy of various fundamental quantities such as the finestructure constant. Detecting or constraining the possible time variations of these fundamental physical quantities is an important step toward a complete understanding of basic physics. High-quality absorption lines seen in the spectra of distant QSOs allow one to probe time variations of several of these quantities. Here we present the results from a detailed manymultiplet analysis, to detect the possible variation of the fine-structure constant, performed using high signal-to-noise ratio, (∼70 per pixel), high spectral resolution (R ≥ 45 000) observations of 23 Mg systems detected toward 18 QSOs in the redshift range 0.4 ≤ z ≤ 2.3 obtained using UVES at the VLT. We validate our procedure and define the selection criteria that will avoid possible systematics using a detailed analysis of a simulated data set. The spectra of Mg doublets and Fe multiplets are generated considering variations in α and specifications identical to that of our UVES spectra. We show that our Voigt profile fitting code recovers the variation in α very accurately when we use single component systems and multiple-component systems that are not heavily blended. Spurious detections are frequently seen when we use heavily blended systems or systems with very weak lines. Thus we avoided these system while analysing the UVES data. To make the analysis transparent and accessible to the community for critical scrutiny, all the steps involved in the analysis are presented in detail. The weighted mean value of the variation in α obtained from our analysis over the redshift range 0.4 ≤ z ≤ 2.3 is ∆α/α = (−0.06 ± 0.06) × 10 −5 . The median redshift of our sample is 1.55 and corresponds to a look-back time of 9.7 Gyr in the most favored cosmological model today. The 3σ upper limit on the time variation of α is −2.5 × 10 −16 yr −1 ≤ (∆α/α∆t) ≤ +1.2 × 10 −16 yr −1 . To our knowledge this is the strongest constraint from quasar absorption line studies to till date.