Spin–orbit torque facilitates efficient magnetisation switching via an in-plane current in perpendicularly magnetised heavy-metal/ferromagnet heterostructures. The efficiency of spin–orbit-torque-induced switching is determined by the charge-to-spin conversion arising from either bulk or interfacial spin–orbit interactions or both. Here, we demonstrate that the spin–orbit torque and the resultant switching efficiency in Pt/CoFeB systems are significantly enhanced by an interfacial modification involving Ti insertion between the Pt and CoFeB layers. Spin pumping and X-ray magnetic circular dichroism experiments reveal that this enhancement is due to an additional interface-generated spin current of the non-magnetic interface and/or improved spin transparency achieved by suppressing the proximity-induced moment in the Pt layer. Our results demonstrate that interface engineering affords an effective approach to improve spin–orbit torque and thereby magnetisation switching efficiency.