The fuel filter was changed and the tensioner was deemed normal so there we go, I'll live with the whine.
Nikos: If this will bother you, then I suggest you have the car sent to BMW for a health check to have your mind at peace.
I have a hesitant start on mornings when it is very damp (doesn't happen on a very cold dry morning though) so I think it might not be something to worry about.
cheers
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