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Check the toothed wheel on the rear driveshafts, they corrode and expand then start chafing the speed sensor , so creating a larger air gap causing false activation around 30-50mph.
BMW only sell complete driveshafts but I know many people that have successfully changed the pick up ring available from Eurocarparts or ebay.
Fast forward to 7.35 on the video to see the corroded ring and shiny at the high spots, you will probably need a new sensor as well.
https://www.youtube.com/watch?v=1PdnFRMMnEQ
Traction Control light and Tyre Pressure light popping up when I went to Screwfix today. Its happened at the same point a few times previously - I'm assuming its the speed sensor either dirty or throwing a fault. Annoyingly the car doesn't tell me which tyre has the pressure drop so I don't know what sensor it is.