Rubbing is due to the offset of the wheel usually and whether you have standard drums or discs/spaced drums as the wider track causes the wheel to be further out
(Assume you have discs at the front or spaced drums to match the rear ones?)
Changing wheel width may help but does depend on the wheel offset still i.e you may get a 5x10 wheel with a lower offset to work - your wheels may be "drum" offset, designed to look wide on standard non-spaced drums but using them on discs/spaced drums they are too "sticky-out" and cause rubbing
I use older 6x10 wheels on both my minis (discs/spaced drums) but with low-ish offset - newer 6x10 seem to have higher offset to give the fashionable wide "stance"
The only time I get slight rubbing is in reverse - to give perspective my wheels don't look any wider than yours on the outside and still fit under standard mini special arches like yours.
You have high-low height adjuster(s) at the rear (at least the side in the picture does ) but can't tell you anything else much without more pics/details
The shocks maybe G-max (if the yellow paint is OE) which is a budget, slightly uprated shock (I use them and find them OK but maybe not everyone's choice)
If you have high-lows all round you could try raising the suspension slightly as that might alleviate some of the rubbing (but that may bugger up other suspension settings (if they were correctly set originally)