Unless it is an R55/R56 where there are many more combinations due the fact the locking bolts are made by McGards and the key is likely to have to be ordered in. Even so, the dealers don't actually seem to know how to identify the right key so it may not be that simple.....I was told on Saturday that there is a number on the key (which there isn't) and of course if you have lost the key you wouldn't have the number anyway!!
There seem to have been far fewer variants for the locking bolts used on the pre R56 minis so the dealers tend to have a stock of all the key types.
My R56 arrived without the little card that gives the McGard key number. But the dealer was able to identify the key by trying the ones in his master set until he found one that fitted. He then ordered me one using the master key number.
If you have not got a card with the number on, take the car to the dealer and get them to do what they did for me.