The room temperature intrinsic strain rate sensitivities (SRS) of basal and prismatic slip systems have been determined for the α (HCP) phase of a titanium alloy (Ti-6242), through coupled crystal plasticity modelling and micro-pillar compression experiments. Load-displacement data from displacement hold tests, in both experiment and simulation, have enabled determination of the rate-dependent slip rule within the crystal plasticity model. Slip system SRS has been obtained, via micro-pillars orientated for single basal and prismatic slip. Crystal plasticity modelling explicitly captures micro-pillar geometry, crystal orientation, as well as the stiffnesses of components of the experimental testing frame and sample mounting. Consideration of the stiffness of the adhesive and load frame is shown to be essential for extraction of the intrinsic rate-dependent material response, rather than the structural response, even in single phase micro-pillar compression experiments. We find that the intrinsic SRS of basal slip is stronger than that for prismatic slip. This finding has significant implications in understanding the anisotropic rate-dependent response of hexagonal materials applied extensively under extreme loading conditions.