Can't understand why anyone would want their car to do this. Very strange. It's best if the car runs properly, surely.
I'm pretty sure even if a car is running properly, it can still pop through the exhaust.
As mentioned, fuel injected cars don't do it as much as carb'd cars.
I suppose, on a standard mini, it probably 'shouldn't' do it, but its not really a problem or anything IMO.
Even with high-overlap cams Mini engines should not back-fire through the exhaust if the ignition, mixture and timing are correct. If my car started to backfire, and it has a 115 bhp 1310 cc rally engine, it would be back on the rollers to be corrected straight away. Any regular backfiring is the sigh of a poorly set-up engine.