From the references I have dug in, it seems that no explanation for the cause of Meisner Effect exists besides the phenomenological london equation that says that the bulk energy is reduced with zero interior magnetic field.
Have I not looked at the right places or is it true that the phenomenological london equation is all we have till now?
The Meissner effect is predicted by the BCS theory of superconductivity (and should, indeed, be predicted by any theory of superconductivity). See e.g. this question for further discussion.
This is not true.
There is a more complete phenomenological theory, the Ginzburg-Landau theory, from which you can derive the London equations. The Ginzburg-Landau theory can in turn be shown to be a good approximation of BCS close to the superconducting transition. Wikipedia has more details and links to the theories and relevant papers.
Furthermore, there are quantum field theoretic arguments for the Meißner effect. (Roughly, that the photon gains a mass in a superconductor due to the breaking of gauge symmetry and therefore the range of the electromagnetic force gets finite, being suppressed exponentially beyond the scale length).
