The petrol pump is a known problem in second-generation MINIs. You can recognize the problem from a cold start that starts with a few cylinders and after a number of counts starts spinning on four cylinders. Check Engine Code P2880
The symptoms are usually:
- Rough cold starts
- Stalling on start
- Rough running
- Running lean
- Intermittent misfires
- Check Engine Code
- P2880 High-Pressure System Code
There isn't an exact mileage that the HPFP begins to fail at. It's common for these to fail as early as 40,000 miles. At around that mileage, I'd begin watching for the symptoms above.
If you decide to tackle this job yourself, it's not too involved. On a scale of 1-5, this falls perfectly in between. Anyone with basic tools and wrenching abilities can complete it in around 3 hours.
The following video is a good example on how to replace it: