My Dad had this same problem with his Merc. Make sure you get to it before the whole thing collapses on your key, otherwise you'll have to park it with the key in the ignition, and the car probably won't be there in the morning!
He fixed his up just as the key started to get sticky. He had to give Mercedes his VIN and they sent him a tumbler that matched his original keys.
Not sure if the same applies for BMW, but i don't see why not. It's a fair bit more expensive (not sure exactly how much more) than getting a new tumbler with a different key.