In this work we report for the first time measurements of the dielectric loss of single-crystal SrTiO3 under the application of hydrostatic pressure up to 20 kbar and temperatures down to 200 mK which allow us to comment on the evolution of new fundamental material properties and their relationship with the recently discovered quantum critical phenomena in this material. The well known 18 K peak or shoulder was no longer observed after pressure was applied, even after subsequently removing it, suggesting it is associated with the twin walls formed at the 110 K cubic-tetragonal transition. The family of familiar peaks were all seen to increase in temperature linearly with pressure and the height of the 9.4 K peak was drastically suppressed by even the smallest pressures. This peak is discussed in the context of a postulated ferroelectric quantum critical point in SrTiO3 and the behaviour of its size linked to the position of this point on the recently established phase diagram.