I do not know what faults are logged in the computer
the first step in diagnosing the cause of safety mode is to have the faults read from the car. This is your first/next/only step.
in terms of possible causes, yes, an worn out transmission can cause this, but so can low fluid, a failed sensor, a voltage problem, etc.
so, you MUST have the faults read as a first step
worst case, if the transmission is worn internally, then you will be looking at approximately £2000 to have your transmission rebuilt or a used unit fitted. Or, approx. £4500 to have a replacement from BMW fitted.
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Thank you, XXXXX XXXXX have the faults read from the car and take it from there as you advised.