We study the clustering of matter in the intergalactic medium from the Lyman α forests seen in the spectra of pairs or groups of z~ 2 quasars observed with FORS2 and UVES at the VLT-UT2 Kueyen ESO telescope. The sample consists of five pairs with separation of 0.6, 1, 2.1, 2.6 and 4.4 arcmin and a group of four quasars with separations from 2 up to 10 arcmin. This unprecedented data set allows us to measure the transverse flux correlation function for a range of angular scales. Correlations are clearly detectable at separations smaller than 3 arcmin. The shape and correlation length of the transverse correlation function on these scales are in good agreement with those expected from absorption by the photoionized warm intergalactic medium associated with the filamentary and sheet-like structures predicted in cold dark matter-like models for structure formation. At larger separation no significant correlation is detected. Assuming that the absorbing structures are randomly orientated with respect to the line of sight, the comparison of transverse and longitudinal correlation lengths constrains the cosmological parameters (as a modified version of the Alcock & Paczyński test). The present sample is too small to have significant constraints. Using N-body simulations, we investigate the possibility of constraining Ω_Λ from future larger samples of quasistellar object pairs with similar separations. The observation of a sample of 30 pairs at 2, 4.5 and 7.5 arcmin should constrain the value of Ω_Λ at +/-15 per cent (2σ level). We also use the observed spectra of the group of four quasars to search for underdense regions in the intergalactic medium. We find a quasi-spherical structure of reduced absorption with radius 12.5 h^-1 Mpc, which we identify as an underdense region.