This data was collected as a part of the UK CCS Research Centre Call 2 Project C2-197: Multi scale characterisation of CO2 Storage in the United Kingdom. This is tabular data and X-ray imagery of drainage and imbibition relative permeability measured on reservoir rocks from the S. North Sea, N. North Sea, and E. Irish Sea of the Offshore UK. The data were obtained through measurements made at two distinct flow rates to allow for an evaluation of the impact of rock heterogeneity. Full details of the rock properties and experiments can be found in Reynolds et al. (2018) reference 3 below, the Final Report of the Project, as well as in the PhD Thesis of Catriona Reynolds with full references given below. Any use of the data should reference the journal article, reference 3 below. Geographical Area - Bunter sandstone in S. North Sea, Cleethorpes-1 Well, 1312.7-1316.1 m depth; Ormsirk sandstone in E. Irish Sea, Block 110/2a, 1247.9-1248.1 m depth; Captain sandstone in N. North Sea, Well 14/29a-3, 2997.6-3005.1 m depth. References 1. Imperial College London and British Geological Survey, Multiscale Characterisation of CO2 Storage in the United Kingdom, UKCCSRC Call 2 Project Final Report, 2016 2. Reynolds, C. Two-phase flow behaviour and relative permeability between CO2 and brine in sandstones at the pore and core scales, PhD Thesis, 2016, Imperial College London. 3. Reynolds, C.A., Blunt, M.J., Krevor, S. 2018, Multiphase flow characteristics of heterogeneous rocks from CO2 storage reservoirs in the United Kingdom, Water Resources Research, 54, 2, 729-745