Because the bottom end is fairly strong and the engine is small, it can live at 7,000 rpm with good preparation. (more with custom parts.) I don't know the factory redline for something like a 1275 Cooper S but I imagine it's something around 6000-6200 rpm, and other 1275's around 5500 rpm.
But, the trick would be to get it to rev to 7,000 rpm, since breathing is going to be the barrier with that. Better flowing head/induction/exhaust and fuelling to match will be needed, along with a camshaft to let it rev that high. But most of those mods will reduce torque on the low end and make the engine peakier. The stock redlines are probably less about the physical limit of the bottom end and more about the lack of breathing to get much higher than the "limit."
The smaller available valve area for a long-stroke engine is the main reason they can't rev like a short stroke, all other things being equal. But the smaller valve area increases gas velocity at lower rpms, which makes them more torquey down low.
Now what the stock A/A+ series engines are known for is being able to run at high revs all day long. i.e. on a long motorway trip, you can keep the thing at 5,000+ for hours and it won't hurt the motor. If you have to tackle some steep grades you can shift down and keep it pegged for a long time if you have to, as long as the motor stays cool.
It's just a matter of being OK with with noise and racket that comes from keeping it revved high. That's the main reason some people choose taller (lower numerically) gears, for more comfort. Plus improved fuel economy, as long as you're not lugging the engine.