cooper s if you wanted proper fun. at least you didn't buy the diesel though.
it's okay but you ideally want 200bhp to make it really fun to drive.
Seems to be quite a common problem, unfortunately with no real answers:
https://www.mini2.com/threads/car-laggy-hesitant-lumpy-driving-from-cold.169529
https://www.northamericanmotoring.c...01-r53-cooper-s-idle-troubles-re-visited.html
To answer the original question.... I wouldn't say it feels lumpy but I would agree that its quite gutless at low revs and likes to be held higher in the rev range when in fun mode. But I'd say thats the case for most older cars. Modern cars have much more low down grunt.
If its actually lumpy low down (by which I assume you mean, not very consistent response?) will be spark, fuel or air (intake and exhaust) related but you'd end up replacing loads of parts until something (maybe) fixes it as you'll notice I've just mentioned all the things that make combustion..... A reasonable plan would be to get the necessary tools/software to get the engine data up on your laptop, and take a look through the data. Should be able to start finding some clues.
Depends how lumpy it is whether its worth the faff. Good excuse to drive it harder and avoid the issue
Ignoring the point about whether we should round any hp number above 100 to 200..
I remember driving a Cooper a number of years ago. Thought it was bags of fun, and that was with the 130hp version.
IIRC, it wasn't lumpy, but was rather coarse. Not sure if the OP is referring to that.
If it is genuinely lumpy, then my suggestion is that you run it on non-supermarket fuel for a few weeks. I found that supermarket fuel made my MX5 feel rough low down. Changed to Shell (just the standard 95) and it smoothed out after a few weeks. I now run it only on Shell 95, and it's been perfect since.
When the car is warm, does it idle ok or does it bounce around a bit? When was the last time it had an oil change?