Over the past decade, exciton-polaritons in semiconductor microcavities have revealed themselves as one of the richest realizations of a light-based quantum fluid, subject to fascinating new physics and potential applications. For instance, in the regime of large two-body interactions, polaritons can be used to manipulate the quantum properties of a light field. In this work, we report on the emergence of quantum correlations in laser light transmitted through a fibre-cavity polariton system. We observe a dispersive shape of the autocorrelation function around the polariton resonance that indicates the onset of this regime. The weak amplitude of these correlations indicates a state that still remains far from a low-photon-number state. Nonetheless, given the underlying physical mechanism, our work opens up the prospect of eventually using polaritons to turn laser light into single photons.