In this paper we study the essential role of Darrieus–Landau (DL), hydrodynamic, cellular flame-front instability in the propagation of expanding turbulent flames. First, we analyse and compare the characteristic time scales of flame wrinkling under the simultaneous actions of DL instability and turbulent eddies, based on which three turbulent flame propagation regimes are identified, namely, instability dominated, instability–turbulence interaction and turbulence dominated regimes. We then perform experiments over an extensive range of conditions, including high pressures, to promote and manipulate the DL instability. The results clearly demonstrate the increase in the acceleration exponent of the turbulent flame propagation as these three regimes are traversed from the weakest to the strongest, which are respectively similar to those of the laminar cellularly unstable flame and the turbulent flame without flame-front instability, and thus validating the scaling analysis. Finally, based on the scaling analysis and the experimental results, we propose a modification of the conventional turbulent flame regime diagram to account for the effects of DL instability.