One thing worth mentioning is on all cars not just the mini, if the badges have been there any length of time, when removed can leave a shadow in the lacquer, and no amount of polishing removes it.
This! Plus don't use WD40 on paint, it's got silly amounts of silicone in it which is a painters nightmare!
We use a new filler spreader to lift the badge off, then some prep clean (panel wipe) wash on, wash off until its off. It won't damage the lacquer like some brake clean or thinners will. If you can't get panel wipe an old trick is to use some petrol that's been sat about for a few weeks....
Happy to be corrected on the above but it's just how we do things. My dad has 30 years in the trade