This study presents an algebraic combustion closure for Large eddy simulation (LES) exhibiting attributes of simplicity and simultaneous accuracy under realistic combustion conditions. The model makes use of the interlink between the reaction and dissipation rates in premixed turbulent combustion but relaxes the thin flame assumption by considering finite-rate chemistry effects in the small-scale turbulence structure. The core idea of the approach is to approximate the reaction progress in the unresolved spectrum of wave lengths and to use it within a filtered reaction rate expression. The model is implemented in OpenFOAM 4.0 and is tested on a turbulent, premixed flame behind a bluff-body, applying an LES approach for turbulence modelling. The cross comparison of velocity, temperature and composition data with experiments and a well-investigated combustion model in literature reveals competitive performance of the new model. Especially in the near-field of the bluff body flame, corresponding to thin and moderately thickened flame regions, its ability to capture the flame structure is highly promising. The chosen, partly explicit approach to recover the temperature from the transported sensible enthalpy, involving a strong coupling between filtered reaction and heat release rate, also shows advantages over obtaining the temperature from presumed probability density functions.