I am sure they do. The orignal mini's have owners clubs and they release news letters and magazines. The new shape has a similar but smaller following but i am sure a friend gets a mini magazine
There are two main mini magazines - Mini World - http://www.miniworld.co.uk/ - and Mini Magazine - http://www.minimag.co.uk/.
Both tend to concentrate on 'proper' minis because, lets face it, the new mini isn't a mini at all - it's a BMW.
If you mean new MINIs (like mine) this is the mag for you http://www.gomini.co.uk/
I know what you mean, boognish, about it not being a real mini - but mine goes like a BMW and i wouldn't swap it for an old one if you paid me.