We look for signs of the HI transverse proximity effect in the spectra of 130 quasi-stellar object (QSO) pairs, most with transverse separations in the plane of the sky of 0.1-3Mpc at z~2.2. We expected to see a decrease in Ly{alpha} forest HI absorption in the spectrum of background QSOs near the position of foreground QSOs. Instead, we see no change in the absorption in front of the foreground QSOs, and we see evidence for a 50 per cent increase in the absorption out to 6Mpc behind the foreground QSOs. Further, we see no change in the HI absorption along the line-of-sight to the foreground QSOs, the normal line-of-sight proximity effect. We may account for the lack of change in the HI absorption if the effect of extra ultraviolet photons is cancelled by higher gas density around QSOs. If so, the increase in absorption behind the QSOs then suggests that the higher gas density there is not cancelled by the UV radiation from the QSOs. We can explain our observations if QSOs have had their current UV luminosities for less than approximately a million years, a time-scale that has been suggested for accretion disc instabilities and gas depletion.