Some E51's have traction control, not sure to what extent we could really term it VDC.
One of my series1 E51's has the traction control, it just reduces throttle when there's wheelspin. There is a button in front of the driver's left knee on the dash to turn it off but it used to reset and turn itself back on again after turning the ignition off/on.
I say 'used to' because the button hasn't worked for a long time, in fact I might've disabled the button by accident when messing about testing what was possible with my Launch Diagnsotics gear... I think at the time I was attempting to turn the traction control off by default but instead semi-permanently disabled the 'off' switch (thus achieving almost the opposite of what I'd intended hehe).
Not sure if any E51's have anything resembling true / full fat VDC (the type that brakes different wheels to prevent the car spinning ot etc), just the type of traction control that backs off the accelerator (not even the type that brakes a spinning driven wheel to give pseudo limited slip diff). That said, those with factory cruise do apply the brakes if the radar detects you're catching up to a vehicle in front, even to the point of almost bringing the car to a complete stop if necessary to maintain the distance.
My S1 E51 that does have the traction control is a 3.5 4x4 XL model, has the factory cruise, curtains, extra footwell lights, etc, so I think maybe the original owner ticked most of the option boxes when it was bought new... But it doesn't have what I'd normally term 'proper' VDC.