Dougal, it's just occurred to me that a wire shorted to ground in the loom connecting the oil pressure switch could cause what you are seeing. Most oil pressure switches connect to ground to register the low pressure. My BMW F650GS Dakar motorcycle has had a similar fault - but in that case it was a faulty oil pressure switch. More than once in fact! Have you checked the loom carefully in the engine back, paying particular attention to look for any damage, heated or crushed sections of wiring?

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Wayne
2005 BMW X5 3.0d (b 02/05)
2001 BMW F650GS Dakar (b 06/01)