How old is your car and how many miles on it. CV joints do not usually fail unless the boot tears and grease gets out, and that is obvious to anyone if you look under the car. So first look under the car at the CV boots. Then you say the wheel bolts are tight. Did you check with a torque wrench? Did you take them off and clean things up as described above then carefully rebolt and torque the wheels as described above? Do these first and see if the noise is still there. The only other usual suspects are moving brake pads or wheel bearings.

 

In my other car, this would be a symptom of a CV joint that is not bolted in securely. I'm not sure how everything is held together on the MINI, but it's worth getting under there and checking the fasteners.

Also try shaking the wheel and suspension parts to see if there is any play, and if so where.