Cavity exciton–polaritons are quasiparticles that form when quantum well excitons hybridize with a cavity mode. Here, we carry out photon correlation measurements under continuous wave resonant laser excitation to demonstrate quantum correlations between cavity–polaritons. Our experiments reveal an unexpectedly strong dependence of polariton interactions on cavity–exciton detuning. When the polaritons are predominantly exciton-like, we observe a transition from photon antibunching to bunching as the laser is tuned across the polariton resonance, in agreement with a simple Kerr-nonlinearity model. When the lower-branch polariton energy is tuned to induce a two-polariton Feshbach resonance with the biexciton mode, the degree of polariton antibunching becomes independent of the laser detuning: we explain our finding by invoking a dissipative blockade mechanism arising from large biexciton broadening. Our experiments demonstrate that the strong polariton blockade regime would be achieved by reducing the polariton decay rate by a factor of 10.