A guess: do modern Hornby transformers have short-circuit protection? Why not try the following: connect meter to the output of the transformer, monitor voltage. Place the train on the track and watch for a significant voltage drop.
Also: try another train on that track, measure the resistance across the wheels of the ?suspect? train and compare to a known good one. Maybe you can test the transformer with a 12v lightbulb, 3-6w 12V would be a reasonable test (IIRC the transformers are 12v).
Is it a mix of old and new parts? Could there be a compatibility issue?
Last suggestion, if the problem seems independent of the applied load, the transformer may be faulty.
Oh, the really easy one is to test the mains connection. Just swap the transformer for desk lamp of something, to ensure the problem isn’t faulty mains supply.