I've had 3 Minis over the last 15 years or so, a 53 'S', an 08 'D' and now an 08 'S' Clubman. A common theme in all of them was that the drivers floor mat always slipped off the velcro mounting pads towards then over, or under, the pedals.
I got into the habit of pulling the mat back onto the pads every time I got into the car to minimise the slippage.
Finally I found a fix which has so far held them in place for about 3 weeks.
I used 2 upholstery 'hog rings', Amazon.co.uk
, which I already had for re-upholstering my campervan seats.
They are pushed into the mat around the beading and the slightly raised part of the floor mat under the seat as shown in the photo:
They were quite hard to push through the material as the rings themselves haven't got much of a point, so I predrilled 2mm holes in the fabric. I didn't bend them with the pliers, as they seem to do the job as is.
The picture is taken from the drivers door looking in (RHD)