Mini One Reduced Engine Power

Sounds like pre-ignition or detonation. I had similar symptoms with my old Renault Megane, though without the smoke. Reduced power, jerking, the whole deal. Have you checked the knock sensor? Maybe it's faulty and not adjusting the engine timing properly.

Knock sensor... Interesting. How would I check that? I'm not really a mechanic. Also, what could cause those deposits in the first place?

Checking the knock sensor is tricky without the right equipment. Honestly, I'd just take it to a workshop. The deposits could be from a number of things: low fuel octane, engine tuning gone wrong, or just normal wear and tear. In my case, it was just old age and using cheap fuel sometimes. But since you have smoke, I'd get it checked sooner rather than later.

Just wanted to update you. The workshop confirmed it was deposits in the combustion chamber, like you suspected. They cleaned it, and it seems to be running much better now. Cost me 425€. Thanks for the help!