OK
Since you see the current between two phases on the delta winding, this means the one winding is either at fault, or (more likely) the secondary has a fault - I would guess one high voltage winding has a fault somewhere along its winding to earth (the star point being earthed) or has an inter-turn winding fault.
This phase will be the one corresponding to the branch of the delta connecting both current taking phases (~8A).
Can you flash test the hv windings - ~27-35kV as it may be an insulation breakdown issue, so won't be shown via an insulation resistance test?
If its an inter-turn winding fault it is a little more difficult to detect with an assembled tx.
(The above assumes there is absolutely nothing connected on the hv side - obviously if there is a single phase load/fault in that part of the system it will reflect as a phase-phase load/fault on the primary )