We apply a new model for the spherically averaged correlation function at large pair separations to the measurement of the clustering of luminous red galaxies (LRGs) made from the SDSS by Cabre and Gaztanaga(2009). Our model takes into account the form of the BAO peak and the large scale shape of the correlation function. We perform a Monte Carlo Markov chain analysis for different combinations of datasets and for different parameter sets. When used in combination with a compilation of the latest CMB measurements, the LRG clustering and the latest supernovae results give constraints on cosmological parameters which are comparable and in remarkably good agreement, resolving the tension reported in some studies. The best fitting model in the context of a flat, Lambda-CDM cosmology is specified by Omega_m=0.261+-0.013, Omega_b=0.044+-0.001, n_s=0.96+-0.01, H_0=71.6+-1.2 km/s/Mpc and sigma_8=0.80+-0.02. If we allow the time-independent dark energy equation of state parameter to vary, we find results consistent with a cosmological constant at the 5% level using all data sets: w_DE=-0.97+-0.05. The large scale structure measurements by themselves can constrain the dark energy equation of state parameter to w_DE=-1.05+-0.15, independently of CMB or supernovae data. We do not find convincing evidence for an evolving equation of state. We provide a set of "extended distance priors" that contain the most relevant information from the CMB power spectrum and the shape of the LRG correlation function which can be used to constrain dark energy models and spatial curvature. Our model should provide an accurate description of the clustering even in much larger, forthcoming surveys, such as those planned with NASA's JDEM or ESA's Euclid mission.