Bonnet release cable is broken

George, usually when the cable breaks,it is at the cabin end of the cable and not the engine side. Take a look underneath your your dash, you should be able to see the broken end. Grab a hold with a pair of pliers and pull the end, the hood should pop. There is also the possibility that the cable pulled out of the little bracket at the release lever. You might still open the hood, by holding the sheathing and pull on the cable. A pair of vise grips may make that job easier. I found this little tidbit of information on your Mini on here

"Using a hacksaw blade, you can ease the kidney grills out of the bonnet, this allows you to release the left hand bonnet release by yanking on the cable that runs under the front cross member. You can't get to the right hand one through here though.....

To release the right hand one, pull off the lens cover from the RH headlamp. EEEeek I know!!!!! , but mine didn't break and all i'll have to do is silicon it back on after the plastic clips broke. This reveals a space behind the indicator that allows you to ferret around to locate the release cable that runs over the headlamp and up the inner wing."