As posted on the previous thread about this, LM had (or possibly still have) a booked empties move from Crewe-Northampton at 0415 - around 100ish miles. I believe it's only tuesday to friday.
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Thinking about it, Virgin often drag out the Pretendolino set from Wembley and take it to Crewe and back with a Skoda on the front. It runs (as far as I am aware, with a 5Zsomething headcode), so it's an empties move. That must be a contender.