Ok, taking some advice from other people, we went outside to try and pull the spoiler off.
We used some spacers that are normally used when fitting PVC windows. They are plastic and didn't damage my paint at all. Also, my mini is a 2003 cooper, so it doesn't have the third nut on the inside of the tailgate.
Use some force to push the spoiler up slightly by the third brake light, just so you can fit the first spacer in to the right or the left of the brake light. You shouldn't be able to see the tape yet, although you will have just pushed the spacer through it. You might be able to move the spacer to the left and right, but it will probably be tight.
Gradually push the spacers in next to one another, and once you get to the end of the spoiler, you should be able to see right inside it. Carry on around the end until you get to the actual roof side of the spoiler. By this stage, you can fit a slightly bigger spacer in and you can see the tape stretching between the spoiler and tailgate. You should be able to drag the spacer through the tape for about 3 inches, then put in another spacer, then tear another 3 inches, and so on.
Once you start getting back to the other side of the spoiler, it gets easier and easier until in the end, putting in a spacer will virtually pull the spoiler off the roof. (Make sure you are holding it at this point!)
Anyway, thats how we did it, it might work for you, it might not. I now have a lovely cooper S spoiler painted blue on my white roof. Different, I know.