After eliminating everything else in the system, it was the BM53.

I ended up sending it back to the repairer, they said they had opened it up and couldn't find anything that would be causing a whine. They did say it sometimes happens with the stage 2 repair, mine had the stage 1. Got it back with same issue.
I'm in New Zealand and it was repaired in the U.K. So wasn't a cheap exercise with postage backwards and forwards etc. Waste of time and money.

I ended up buying a known good unit off eBay U.S. for a decent price after keeping an eye out on there for a while.
Fitted it- works perfect now. I fitted an aux socket and couldn't be happier with it.

Wouldn't bother with a repair again.

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2003 E53 3.0
2001 E46 330ci Msport
2001 E46 325i Touring wagon