I cannot help it.

Try tighten the nut behind the steering wheel. Obviously you need a lot more time with the stick and that redundant pedal, as well as understanding the purpose of transmission, engine torque, and how horsepower is interrelated to torque. You should be proud that very few people can drive one these days. My Mini is just about carjack proof that it has a long shifter with the reverse lockout cable removed.

 

pnw makes a good though maybe a little snarky point. Experience coupled with the ability to problem solve takes time. If there's a MINI club in your area I'll bet someone there would be more than glad to sit in on a session and coach. BTW the first car I drove was a '47 Chevy 3 on the tree and my first two cars were British roadsters. My point? Once in a while I miss a shift, clank some gear teeth or some other embarrassing behavior. Just last week I killed it with insufficient throttle out of a parking lot.

 

1st to 2nd with the Midland/Rover tranny is almost never going to be smooth, 3000 to 3500 are good marks to shift at for just puttering around town. If being automatic transmission smooth is your goal, try and feel when the clutch actually engages and disengages. My clutch peddle is very soft with little resistance and little feel. Most of the action is at the top of the peddle travel and I don't actually have to depress the peddle all the way to the floor to make changes, up or down. The Midlands/Rover transmission is very forgiving in this respect.

 

Try double clutching

 

I'd start with a little more rpm.

These little engines don't like to be lugged/heavily loaded at all. They like a little rpm. I try to keep mine above 2800/3000 rpm at all times while moving. I learned this from years of driving high powered (1000cc's and up) Japanese motorcycles. The "little" Mini engine isn't much different. In my year of owning mine (05, JCW), it seems very much like the bike engines, do not lug them. They do not like to be heavily loaded at low rpm.
You know when that happens...you hit the throttle hard, the engine makes a lot of noise, but takes a while to actually get the car moving...that's lugging an engine.
Keep the rpm up a bit so when you have to hit the throttle hard, the engine is actually ready to motivate the car...rpm/power wise. Its closer to being in its power band (rpm vs torque).

Drive at no less than 2800 rpm.
Shift (normal driving) at 4000/4500 rpm. Getting on the freeway, open road, shift at 6000 (or so !) rpm.
When you push the clutch in...push it in fully and quickly.
Shift.
When you let the clutch out, learn to "feel" the engagement point. As has been said, that's IS a little difficult to learn with a hydraulic clutch. Let the clutch out with purpose. Somewhat quickly, but not so much to have it buck and kick (another rpm vs car speed thing). Match the clutch engagement and the rpm as best as you can.

Experiment...learn...remember !

Have fun

Mike

P.S. - NO DOUBLE CLUTCHING..! You are still learning, this is NOT a requirement for a proper shift.