OK, it's not really that hard to understand is it...
These rims are S offset. Cooper S's had spaced drums on the rear and an equivalent track with the front discs.
So the Tempe Tyres rims are designed with this in mind. Therefore you need the same track (front and rear). If you dont have stepped drums, you will need them or spacers.
Because Honda discs are a grey area and non standard, there is a little confusion as to whether they will fit.
Kev, I will come around Sat morning (as mentioned) with a rim to try out on one of your Mini's running Honda's
That will sort it all out.
EDIT: from the look of miniVan's van, they fit perfectly with spacers and flares, as per Cooper S's.