Typically, changing an air filter is easy, but I notice on my Mini 2004 S that the plastic cover housing the filter sits beneath the anti-sway bar. I don't see how I can remove it without having to remove the bar as well. Am I correct, or is there a simple way to remove the air filter? And if I DO need to remove the anti-sway bar is there something I ought to know before I begin? Thanks.

Its not an anti-sway bar; its a strut tower brace.

Indeed, that would be correct. The anti-sway bar is under the car. Still, the problem in the original question remains.

Remove strut tower brace...then open air box and change filter.

I presume you bought the MINI with the strut tower brace? If so, it's not a stock part so you have to remove it then remove the plastic covering for the air filter.

Interesting that the tower brace is not a stock part.
In which case, am I right in assuming that the brace is not under tension, and that once removed it will align exactly as before? Thanks for the suggestions.

That is correct, it is mainly for structural purposes. So go ahead and remove it, you won't have any problems.

Thanks for your help