  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.
