In this work, heavy metals were removed simultaneously using wheat bran as an adsorbent. For batch experiments, the Box-Behnken design of response surface methodology was used and the effect of dye on metal removal was analysed. It has been observed that the presence of dye has reduced the removal of each metal in the range of 100-20% with no appreciable reduction in dye adsorption. The optimum pH, temperature, and adsorbent dose were found to be 7.59, 33.23 °C, and 2.90 g/L, respectively, for 79.70% chromium, 99.9% cadmium and 87.27% copper removal. It was found that Langmuir isotherm fits well with the experimental data (RMSE value up to 0.033). The maximum adsorption capacity obtained for copper, chromium, cadmium and dye were 2.17 mg/g, 1.76 mg/g, 1.52 mg/g and 3.215 mg/g, respectively. The continuous study was performed for parameters, i.e. bed height (0.15-0.45 m), flow rate (5-15 mL/min) and initial metal concentration (100-500 mg/L). In continuous study, dye acted as an interfering species and as a result breakthrough and exhaustion time decreased. The modelling and simulation of continuous adsorption process were performed. A dynamic mathematical model was developed for continuous fixed bed adsorption column to compare the breakthrough curve with experimental results.