We have measured redshifts for 243 z approximate to 3 quasars in nine Very Large Telescope (VLT) Visible Imaging and Multi-Object Spectrograph (VIMOS) Lyman-break galaxy (LBG) redshift survey areas, each of which is centred on a known bright quasar. Using the spectra of these quasars, we measure the cross-correlation between neutral hydrogen gas causing the Ly alpha forest and 1020 LBGs at z approximate to 3. We find an increase in neutral hydrogen absorption within approximate to 5 h(-1) Mpc of a galaxy in agreement with the results of Adelberger et al. The Ly alpha-LBG cross-correlation can be described by a power law on scales larger than 3 h(-1) Mpc. When galaxy velocity dispersions are taken into account, our results at smaller scales (<2 h(-1) Mpc) are also in good agreement with the results of Adelberger et al. There is little immediate indication of a region with a transmission spike above the mean intergalactic medium value which might indicate the presence of star formation feedback. To measure the galaxy velocity dispersions, which include both intrinsic LBG velocity dispersion and redshift errors, we have used the LBG-LBG redshift-space distortion measurements of Bielby et al. We find that the redshift-space transmission spike implied in the results of Adelberger et al. is too narrow to be physical in the presence of the likely LBG velocity dispersion and is likely to be a statistical fluke. Nevertheless, neither our nor previous data can rule out the presence of a narrow, real-space transmission spike, given the evidence of the increased Ly alpha absorption surrounding LBGs which can mask the spike's presence when convolved with a realistic LBG velocity dispersion. Finally, we identify 176 C IV systems in the quasar spectra and find an LBG-CIV correlation strength on scales of 10 h(-1) Mpc consistent with the relation measured at approximate to Mpc scales.