We investigate the quantum coherent dynamics of an externally driven effective two-level system (TLS) subjected to a slow Ohmic environment characteristic of biomolecular protein–solvent reservoirs in photosynthetic light-harvesting complexes. By means of the numerically exact quasi-adiabatic propagator path integral (QUAPI) method we are able to include non-Markovian features of the environment and show the dependence of the quantum coherence on the characteristic bath cut-off frequency ωc as well as on the driving frequency ωl and the field amplitude A. Our calculations extend from the weak-coupling regime to the incoherent strong-coupling regime. In the latter case, we find evidence for a resonant behaviour, beyond the expected behaviour, when the reorganization energy Er coincides with the driving frequency. Moreover, we investigate how the coherent destruction of tunnelling within the TLS is influenced by the non-Markovian environment.