The alarm in question looks like this:
The red light indicates a fault, which is why I’ve finally confronted my inability to remove it (hopefully your smoke alarm fault-free).
I’ve found the Kidde instructions on this to be infuriatingly vague on how you actually detach the unit from the base, so as I had to go through a lot of swearing to work it out, I figured some other people might have the same problem. Why are instruction manuals often so badly written?
The side of the alarm has the arrows to twist clockwise for “off” and anti-clockwise for “on”, but there is a small lug which prevents the unit from twisting. Here’s the lug:
Use a small screwdriver, or other poking device, to push this lug towards the base of the smoke alarm, like so, and you will be able to twist the unit free of the base:
The unit will still be attached to the base by the power plug. The plug has two catches on either site, like this, squeeze them together:
You can see the catches in this photo:
The end. Remember to only remove your smoke alarms temporarily, and refit them as soon as possible!
(N.B: I believe this alarm is discontinued by Kidde.)