The corrosion inhibition behaviour of tannic acid (TA), gallic acid (GA) and their blends on mild steel in 1 M HCl solution was studied via electrochemical methods, namely, polarization (Tafel plots) and electrochemical impedance spectroscopy (EIS). The surface morphology of mild steel in 1 M HCl, TA alone, and in combination with GA was elucidated using scanning electron microscopy (SEM). The results show that TA can protect mild steel from acid corrosion better than GA. However, inhibition effect of TA can be enhanced by its combination with GA. The adsorption behaviour of TA against steel corrosion obeyed Langmuir adsorption isotherm. Furthermore, polarization results suggest that TA and GA blends behaves as mixed-type inhibitor of predominant anodic effect. EIS results reveal that the charge transfer resistance value of the steel inhibited by TA in combination with GA is significantly higher than that of steel inhibited by TA alone. The SEM images confirmed the enhanced film formation on the steel surface in the presence of TA and GA blended in the ratio 9:1 when compared with TA alone. Quantum chemical calculations have been used to provide insights into the mechanism of interaction of TA and GA on mild steel.