I didn’t actually do it today, but was able to verify that it worked today.....
Budget auto-dim rear view mirror
2nd hand 1 series mirror 7118331 for £19.99 compared to the much more expensive ones for e85/86
Do the normal procedure to take off the mirror
Split both mirrors in half
Remove the card which illuminates the clown-nose alarm - this is the remote sensor which works on a different frequency - 433 vs 866 MHz
Swap the e85/86 sensor into the 1 series mirror
Put back together and plug into the car
Enjoy not being dazzled by cars behind you
Terrible quality pics, but at least you can see the difference from when I covered the sensor on the rear