What's the link for the UK website please?
Not sure if it will work as the address appears to contain some necessaries that may be unique to the pc being used but here it is.
Link
If it doesn't work, just go to the uk mini website and click on the person icon at the top right. (It sometimes seems to hide, but it's there next to the magnifying glass)
It pops up this when clicked.
Once you jump through all the hoops to register, you can add your vehicle by clicking the person icon again and then clicking add vehicle. You will need to use your VIN number either from the windscreen or your V5. Both mine and dad's clubman required a verification code which is sent from BMW/Mini to the car itself and can be picked up off the central screen.
Once you have the vehicle added, you can go to your vehicle and find the map update section.
Then you click on "to manual map update". Download the tool and hopefully it should be plain sailing. I applied the update downloaded via this method to both our cars today. It took about 15 mins.