I have a 2004 mini and when I brought it in for a noise it was making at low speeds (at least that is when I could hear it)I was told it was a normal noise from the electric motor of the power assisted steering. I was told that nothing was wrong... It is a high pitched "whirring" noise.
I have not heard this noise from other mini's. Is it a sign of a power steering pump going bad? Or is it truely nothing to worry about? Anyone? Yes, this car is new to me and I am a first time mini owner.

 

My 06 makes the same noise, and I was told it's the power steering as well. it's done it as long as I've had it, since it was brand new, and it does it consistently so I haven't worried about it.

 

i have an 06 as well. and i've been hearing a really high pitched whirring noise that gets louder and quiter when stepping on the gas especially after i installed the piezo buzzer. (the "hi-lo hi-lo" noise when locking the car, which is more of a "woo-wee woo-wee" noise)