The present article deals with the study of interacting and non-interacting dark energy (DE) and dark matter (DM) in the spatially homogeneous and anisotropic Bianchi I space–time within the framework of Brans–Dicke (BD) scalar–tensor theory of gravitation. As the set of field equations is not closed, exact solutions are obtained using power-law relation and assuming a linearly varying deceleration parameter. The physical acceptability and stability of the obtained model are scrutinised using energy conditions and squared speed of sound. The statefinder diagnostic method is adopted to discuss and measure the deviation of the considered model from the $\Lambda$ cold dark matter ($\Lambda$CDM) model.