The later models of the Mini (after about '73) use a mechanical fuel pump driven off the camshaft at the rear of the motor. These pumps are generally reliable but when a diaphragm goes bad it can be very bad as often raw gas is pumped into the engine. This dilutes the oil and causes severe wear.
Long arm pump. Requires spacer between the pump and the block. Order AUB5012. If you need gaskets, CAM6657.
For 1990 on with HIF44 use AZX1817.
For 92 - 94 with HIF38 and 5/16" inlet use WND10005