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I would say that its likely a wheelspeed sensor issue (or something related like alignment) as they are used by both the DSC and the tyre pressure system. If the sensor is loose or damaged it could be being affected when the car is accelerating or going over bumps. On the e90 its also a reasonably common probem that the yaw sensor in the DSC fails which can cause the traction control light.
The lights are quite general and could mean a lot of things though. The garage should be able to pull the chassis codes and isolate the problem (FWIW you can download a tool called BMW scanner and read them using a laptop at home).
Anyway, good luck with it!
It’s a 3 series e90. All tyres are less than a year and I’ve done sub 5k on them so no real wear.
The traction control warning is always below 30mph, occurring more often at slow speeds when I attempt to accelerate or travel over a few bumps in the road at slow speeds.
I’m hoping it a faulty sensor and not a replacement drive shaft.
I’ve managed to get it into a garage first thing so will report back - I don’t have the time to diagnose or fix so opted for the easy/potentially expensive route.