The phase diagram and critical properties of the $N$-component London superconductor are studied both analytically and through large-scale Monte-Carlo simulations in $d=2+1$ dimensions (components here refer to different replicas of the complex scalar field). Examples are given of physical systems to which this model is applicable. The model with different bare phase stiffnesses for each component, is a model of superconductivity which should arise out of metallic phases of light atoms under extreme pressure. A projected mixture of electronic and protonic condensates in liquid metallic hydrogen under extreme pressure is the simplest example, corresponding to N=2. These are such that Josephson coupling between different matter field components {\it is precisely zero on symmetry grounds}. The $N$-component London model is dualized to a theory involving $N$ vortex fields with highly nontrivial interactions. We compute critical exponents $\alpha$ and $\nu$ for N=2 and N=3. Direct and dual gauge field correlators for general $N$ are given and the N=2 case is studied in detail. The model with N=2 shows two anomalies in the specific heat when the bare phase stiffnesses of each matter field species are different. One anomaly corresponds to an {\it inverted} \xy fixed point, while the other corresponds to a \xy fixed point. Correspondingly, for N=3, we demonstrate the existence of two neutral \xy fixed points and one inverted charged \xy fixed point.