Can the injection not be done from the outside?

It is done from the outside. However, it requires the plaster inside to be
replaced, as it will be damaged and contaminated with salts or something.
Besides, it creates additional work for the damp proofing specialist.

OTOH, you seem to suggest the the inside floor is lower than the outside
ground. That would require tanking up to above the DPC layer, as there would
be no protection against rising and penetrating ground damp below the DPC
layer.

Of course, if it is condensation, rather than penetrating or rising damp,
none of this will help. However, the fact it is concentrated solely in the
very bottom of the wall might suggest a penetrating problem. However, I
suppose it could just be the proximity of the cold ground that causes a
condensation problem.

I assume you don't have/do anything silly, like unflued gas heating or
constantly drying clothes indoors?

Christian.