This dataset contains (1) measurements of the settling dynamics of spheres, disks and rods in non-ionic and ionic aqueous solutions containing 1 g/L of xanthan gum (XG) and cappa-carrageenan (CR), (2) rheological characteristics of these non-Neatonian dispersions. Individual salts -NaCl, KCl, and CaCl2 and a mixture of salts corresponding to seawater were used in the study. Overall, five solutions with dispersed XG and five solutions with dispersed CR were considered. The sinking of six types of plastic particles with dimensions not exceeding 5 mm was examined in a settling column using visualisation and Particle Tracking Velocimetry methods to achieve data on the position of particle centroid in time. Rheological measurements were carried out to assess flow properties. Experiments on settling dynamics were conducted at the Laboratory of Hydrodynamic Micromodels, Institute of Geophysics, Polish Academy of Sciences and rheological measurements at the Faculty of Chemistry, Warsaw University of Technology.