Dissipation-free photon-photon interaction at the single photon level is studied in the context of cavity electromagnetically induced transparency (EIT). For a single multilevel atom exhibiting EIT in the strong cavity-coupling regime, the anharmonicity of the atom-cavity system has an upper bound determined by single atom-photon coupling strength. Photon blockade is inferred to occur for both single and multi-atom cases from the behaviour of transition rates between dressed states of the system. Numerical calculations of the second order coherence function indicate that photon antibunching in both single and two-atom cases are strong and comparable.