As in not unleaded / lead-free? NO. All MINIs are built to take unleaded / lead-free gasoline, and CANNOT, under any circumstances, take regular leaded petrol.
If you refer to the octane levels available in lead-free gas, the MINI can take anything from 91-98 octanes, although the higher the power of the MINI, the more recommendable it is to use higher octane gas. -This is only partly true.... The higher the octane, the less likely the gas is to prematurely ignite in the combustion chamber under compression. Due to design of the MINI's engine (both standard and S type), the compression ratio is higher in the MINI than most other vehicles. Because of this regular gasoline, octanes 85-87 depending on what state you live in, has a tendancy to ignite prematurely during the compression stroke of the engine. To compensate for this, the onboard computer in the MINI will retard the ignition timing. The result of this decreased power output and a possibility of knocking. In short, you CAN run regular gas, but you may notice sluggish engine performance. MINI's are tuned to run on gas with an octane rating of 91 or higher. However, higher octane does not equal more power. Stock MINI's are intended for street use and running anything higher than 92 or 93 will not result in an appriciable increase in power, if any at all.