We present an efficient strategy to modulate tunnelling in molecular junctions by changing the tunnelling decay coefficient, β, by terminal-atom substitution which avoids altering the molecular backbone. By varying X = H, F, Cl, Br, I in junctions with S(CH2)(10-18)X, current densities (J) increase >4 orders of magnitude, creating molecular conductors via reduction of β from 0.75 to 0.25 Å-1. Impedance measurements show tripled dielectric constants (εr) with X = I, reduced HOMO-LUMO gaps and tunnelling-barrier heights, and 5-times reduced contact resistance. These effects alone cannot explain the large change in β. Density-functional theory shows highly localized, X-dependent potential drops at the S(CH2)nX//electrode interface that modifies the tunnelling barrier shape. Commonly-used tunnelling models neglect localized potential drops and changes in εr. Here, we demonstrate experimentally that [Formula: see text], suggesting highly-polarizable terminal-atoms act as charge traps and highlighting the need for new charge transport models that account for dielectric effects in molecular tunnelling junctions.