Robin, having made my first journey with the Berli, and suffered with a heat related refusal to start, I thought of your issue.
Might it be related to ethanol? I am guessing your engine isn't the latest, perhaps an early fuel injection unit, I don't 'know' the BMW engine types so please excuse my ignorance but I wonder if your problem might be related to vapour locking? On the face of it that seems to match the symptoms you describe, it won't lave a fault code and self corrects once the engine has cooled.
At least worth a thought?
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