Magnetic tyre char (MTC), activated tyre char (ATC) and commercial activated carbon (CAC) were used as packing materials in lab-scale column study for the adsorption of three pharmaceuticals: propranolol (PRO), ciprofloxacin (CIP) and clomipramine (CLO), from aqueous solution. The obtained breakthrough curves (BTCs) suggest that, lower flow rate, greater bed height, higher pH and nano particle size led to increased adsorption of PRO. The lowest adsorption capacity was observed for CIP either from single or ternary solution while it was significantly higher for CLO. Surface area of ATC increased nearly twelve-fold (38.17 to 453.81 m²/g), after thermal and chemical activation and adsorption capacity was comparable to commercial activated carbon. The suitability of Hydrus-1D model incorporating chemical non-equilibrium process to simulate the pharmaceutical transport and fit experimental BTCs was demonstrated (97.29 <R² <99.22) in comparison to other common models (Adams–Bohart, Thomas and Yoon–Nelson). The modelling suggests the existence of non-equilibrium conditions and rate-limited sorption sites and the effect of dispersion and mass transfer mechanisms in the solute transport under dynamic conditions. The cost analysis showed that unit cost for treatment of wastewater using fixed-bed columns of tyre char was calculated to be 1.57 US$/m³ which can be deemed as commercially feasible.