Touch wood I don't have this but I did have it on my F20 (M140i). And I wasn't the only one. Sounds very familiar.
The comment about the F30 reminded me that we looked at all sorts on babybmw forum.
Came down to either new steering rack, top mount or a loose bolt on the steering rack. Info below: BMW eventually brought out a fix for the steering rack.
Impacted both left or right sides.
For me, initially the steering rack bolt was loose. Had it tightened, steering improved and noise was quieter but not gone.
Then my top mount exploded at 70mph on the motorway. Managed to get her to a BMW dealer nearby. They fixed under warranty and no noise ever again so was defo the top mount. Ironically I had taken her in 2 days before for them to check it. BMW said it's fine.
https://www.babybmw.net/forum/viewto...4&t=110735