Check that the pedal is returning to its stop freely. There is no return spring on the pedal if you have a servo, however for anyone without a servo who has similar problems, the spring should be the first thing to check. They do sometimes break, and you must never drive without it, as bad things will happen.
Because you have a servo, the equivalent spring is in the servo, and has the same function, pushing the servo pushrod outwards, and so pushing the pedal up. Again, the spring may be defective, but it is more likely to be a problem in the linkage. Or, the servo could be faulty, but I would advise checking the linkage, and removing, cleaning and greasing everything including the pedal shaft. Worst job on a Mini, but it does need doing from time to time, and you will have the peace of mind that you will not need to do it again for maybe 10 years, once it is done. Do the clutc pedal too of course, a few extra moments is all it will take now, rather than have to do it all again later. You may want to fit a new clevis pin, as they do wear, while you are in contortions.
Also, check for silly things like the brake light switch, if the adjustable type, being set wrongly and preventing the pedal from returning fully.
Whatever the cause, I fear that you are going to have to be a contortionist to check things out properly.The usual approach to pedal problems is to take the driver's seat out, a 2 minute job as you likely know, place a flat board or some good padding on the floor, over the crossmember, and WEARING GOGGLES (don't want to drop bits in your eyes, which is VERY likely), lie on your back, feet up on the back seat, head under parcel shelf. You could also try raising the car very high, and standing outside with door open, or better, removed.