Sorry about your MINI. We learned with our first MINI, the handbrake is purely mechanical, no power assist, and operates on disk brakes.
A token tug on the lever is not enough. If you want the hand brake to be effective, a very firm pull on the lever is needed. Sherry's right arm is larger than her left, and I attribute that to the daily handbrake workout.
The brake should be set with enough force that in order to release it, you must pull up on the lever while depressing release button. If you can push the button, and the lever falls down, you did not set the brake firmly enough.
