These datasets contains the flow profiles and time histories produced by the FV1, MUSCL-FV2, DG2-NL and DG2-LL for the following tests: Sec. 2.3: Analytical assessments of model conservation properties: Time histories of normalised total energy and mass error from FV1, MUSCL-FV2, DG2-NL and DG2-LL at 20m and 40m grid resolution. Water level profiles at 7tau/2 and 8tau from FV1, MUSCL-FV2, DG2-NL and DG2-LL at 40m grid resolution, along with the analytical solutions. Sec. 3: Comparison against industrial flood model outputs Sec. 3.1.1: Flooding and drying cycle over a sloping topography: Time histories of water level from DG2-LL and DG2-NL at 10m resolution, DG2-NL and MUSCL-FV2 at 20m resolution, and the reference solution. Sec. 3.1.2: Symmetrical flow propagation over a flat bed: Time histories of water level and velocity from from DG2-LL and DG2-NL at 5m resolution, DG2-NL and MUSCL-FV2 at 10m resolution, and the reference solution. Sec. 3.1.3: Slow filling of multiple ponds: Time histories of water level from from DG2-LL and DG2-NL at 20m resolution, DG2-NL and MUSCL-FV2 at 40m resolution, and the reference solution. Sec. 3.2.1: Momentum conservation over an obstruction: Time histories of water level and velocity from from DG2-LL and DG2-NL at 5m resolution, DG2-NL and MUSCL-FV2 at 10m resolution, and the reference solution. Sec. 3.2.2: Torrential flooding over a rural catchment: Time histories of water level and velocity from from DG2-LL and DG2-NL at 50m resolution, DG2-NL and MUSCL-FV2 at 100m resolution, and the reference solution. Sec. 3.2.3: Dam-break over an oblique building: Time histories of water level and velocity from from DG2-LL and DG2-NL at 0.1m resolution, and DG2-LL and MUSCL-FV2 at 0.2m resolution.