I live in Australia and I've ordered parts before, generally no trouble at all.
Last year I visited the UK and was lucky enough to attend the National Mini Cooper Day at Beaulieu (I think I'm actually in a photo somewhere on here

). I bought quite a few parts, including a whole 7.5" disk brake kit from the Minisport stand at the Cooper Day. A very nice chap at KAD helped me over the phone with a few small parts and I even got my VAT refund from him shortly after I returned to Oz, plus the nice man at the BA counter at Heathrow let me sneak my 29 kg suitcase on the flight home without penalty.
Unwrapped some of the smaller brake kit parts recently as I finally start putting bits of my car together and realised the splines haven't been machined into this drive flange

and it's not like I can pop in for a replacement. Oh well, live and learn eh?

I tend to order elsewhere now.
(Was still a great trip - you lot aren't as bad as people make out

)