Hi, I just put a new clutch in my gen. 2 Mini One 1.6. I followed your procedure and took the radiator/service unit right off the car but didn't take the subframe off. Then I lowered the engine a couple of inches and pulled it forwards a couple if inches and got the transmission out, it was a bit fiddly especially putting it back but saved a few hours.
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Mini R56 Clutch Replacement | R56 Cooper (2007-2013) | Pelican Parts DIY Maintenance Article