We show, that photon non-linearities in electromagnetically induced transparency can be at least one order of magnitude larger than predicted in all previous approaches. As an application we demonstrate that, in this regime they give rise to very strong photon -photon interactions which are strong enough to make an experimental realization of a photonic Mott insulator state feasible in arrays of coupled ultra high-Q micro-cavities.PACS numbers: 03.67. Mn, 42.50.Dv, 73.43.Nq, Introduction: Various quantum mechanical effects have been observed with photons. Examples include quadrature squeezing and entangled photon states [1]. All these effects require strong non-linear interactions between photons for their observation. Unfortunately, photons tend to interact only weakly and it is thus of considerable interest to develop schemes achieving larger and larger photon non-linearities, as these would make further quantum effects accessible in experiments.A scheme for the generation of a large photon nonlinearity has been proposed by Imamoglu and co-workers [2] for atoms with a level structure considered in electromagnetically induced transparency (EIT) [3], which interact with the resonant light mode of a cavity and in [4] it was clarified when this is strictly a photon-photon interaction. Non-linearities obtained in this way can be strong enough to employ them as single photon turnstile devices [5]. The photon non-linearity considered in [2] can be studied in a more general regime as a nonlinear interaction for dark state polaritons [6]. This nonlinearity and other approaches [7] have been employed to show that effective many body physics should be observable in arrays of coupled cavities [6].In this letter, we show, that the photon non-linearity proposed in [2] exists in a much more general parameter regime than previously considered [4]. In that way, we can relax a restricting assumption used in [2,4] and [6] and are thus able to increase achievable photon-photon interactions by at least one order of magnitude. As the non-linear interactions presented here are significantly stronger than in previous schemes they open up possibilities for the observation of phenomena which were previously not accessible in experiments. If generated in an array of coupled ultra high-Q micro-cavities [8], they can become large enough to make the experimental observation of a Mott insulator state for photons rather than polaritons feasible.The parameter regime we consider in this paper is crucially different to the dark state polariton regime employed in [6] and the regime addressed in [7]. Indeed, the non-linearity we derive here is an interaction between photons and not polaritons (joint atomic -photonic ex-