Of course these currents must expel the applied magnetic field completely when the charge carriers are not scattering; this is just simple first year physics (Lenz' law- have you heard about it?) and do not require a "non-trivial" calculation based on virtual physics; based in turn on manipulations of the phase of a so-called order parameter (Bose-Einstein condensate)
The arguments based on London theory which uses the order parameter is pretty simple. They are not real derivations because by writing down the effective theory you almost put in the effect by hand. This is similar to the Higgs effect: Photons become effectively massive and em-fields don't propagate inside the superconductor.
I'm talking about a derivation from a funbdamental theory like BCS theory,
see e.g. here. You can't just say: Let's assume that the electrons don't scatter. Then you also put in the desired result in by hand. You have to start from some realistic microscopic model that describes the electrons in the metal and then show that you indeed have the Meissner effect. This is done in the book by Rickayzen (and in many other books, but I happened to have read that book).
