I just got done fixing mine. The culprit was a slipped axial spring by the key-lock mechanism in the seat
. Yep, it's likely that nothing is broken, just a bad design, I'm looking at you MINI. It's not pretty to get at, but the repair is fairly straightforward.
Labeled pictures can be found here
The first task is getting the seat back out. I tried several different ways to "alternatively actuate" the latch from the back, but couldn't see anything and couldn't come up with an appropriate tool. The nature of the failure doesn't let you grab the cable with pliers and pull. The cable is totally useless at this point.
So, I went in from the front. To get at the latch mechanism, you have to partially pull off the upholstery. Luckily, it is not nearly as bad as it sounds. The upholstery has a plastic edge that presses into a seam on the back side of the seat pan. You just start at the top of the seat, and start pulling the edge out. You can do it with just your fingers. I'm afraid as time goes on and the cloth gets worn, things may rip, but my '05 interior has held up quite well..... even in AZ. Anyway, separate the edge as much as you can from the top, around the upper right corner and down the right side. Maybe you can get away with just pulling away the top.
Pull back the top and right corner of the upholstery and padding. Again, maybe you can get away with just pulling away the top.You just want to get enough access inside the seat to see in at the top left corner with a flashlight. What you'll see is a metal ear with a hole in it. Take a coat hanger, put a small hook in the end, fish it into the corner, hook the hole and pull the ear up. Your seat will unlatch.
Once you have the seat back removed, pull back the upholstery from the upper left corner and remove the two Torx bolts. Bend back the upholstery, hold on to the plastic key lock housing from inside and pull it straight off the latch assembly. There are no screws hold them together, its just a press fit of plastic onto two posts.
You can now see the top where the cable end is attached. You will see the axial spring and it will more than likely be resting on the metal housing instead of the plastic lever where it should be. I just put the spring back on which is dumb because this failure is bound to occur again in the future. If I have to do it again, I will probably heat up a small piece of pin and push it into the plastic behind the spring flange with it sticking up about two spring wire diameters. This would act as retainer and probably keep the pin from wiggling off again.
Look at the annotated pictures linked above for more info. Good luck.