This is the part that you mentioned. Not exactly a thorough description on that site!

CABLE - Super Specials - Cooper BMW Parts, Inchcape

I suspect this is also suitable but it too doesn't have an image.

www.bmminiparts.com - Part Details

And then finally this one, which I'm most confident about buying.

www.bmminiparts.com - Part Details

I presume there is room behind the head unit for these 'straight in' type connectors and I wouldn't need some sort of right angle adaptor?