A series of Direct Numerical Simulations (DNS) of lean methane/air flames was conducted to investigate the enhancement of the turbulent flame speed and modifications to the reaction layer structure associated with the systematic increase of the integral scale of turbulence l while the Karlovitz number and the Kolmogorov scale are kept constant. Four turbulent slot jet flames are simulated at increasing Reynolds number and up to Re ≈ 22, 000, defined with the bulk velocity, slot width, and the reactants’ properties. The turbulent flame speed ST is evaluated locally at selected streamwise locations and it is observed to increase both in the streamwise direction for each flame and across flames for increasing Reynolds number, in line with a corresponding increase of the turbulent integral scale. In particular, the turbulent flame speed ST increases exponentially with the integral scale for l up to about 6 laminar flame thicknesses, while the scaling becomes a power-law for larger values of l. These trends cannot be ascribed completely to the increase in the flame surface, since the turbulent flame speed looses its proportionality to the flame area as the integral scale increases; in particular, it is found that the ratio of turbulent flame speed to area attains a power-law scaling l0.2. This is caused by an overall broadening of the reaction layer for increasing integral scale, which is not associated with a corresponding decrease of the reaction rate, causing a net enhancement of the overall burning rate. This observation is significant since it suggests that a continuous increase in the size of the largest scales of turbulence might be responsible for progressively stronger modifications of the flame’s inner layers even if the smallest scales, i.e., the Karlovitz number, are kept constant.