I have a 2012 BMW 3 series. I recently had two tyres replaced in a tyre
and exhaust centre, and the man told me that both my front and rear
brakes were worn and should be replaced within weeks.

Yet the car itself is telling me that there are at least 6000 miles left
before brake replacement is necessary. Which advice is likely to be more
reliable? If the brake pads are dangerously worn, will the car's warning
lights alert me?