Have a Check Engine light on and throwing codes, this might be your anwser. The Oxygen sensor in your MINI reads the fuel air mixture and calculated to the ECU what fuel level mix is optimum for performance. These units are the heated type, this one is for pre catalytic.

You can tell your O2 sensor is on its way out before the CEL when you see your gas mileage drop dramatically.

Also referred to as a Lambda Probe.