Steeve, I had an R56 Cooper courtesy car for a few days, and found that below 2k rpm in 4th (around 30ish) it was so unresponsive, barely pulling away at all, sounds like the car I had was similar to yours.
My R56S is fine at 30 in 4th, it doesn't struggle and pulls away strongly. Dont remember my r50 cooper being anything like as unresponsive as the new cooper (that i drove anyway) at these low revs.