I intend leaving the small round fitting in place. Can I chop off the flex (with the mains turned off obviously!) and tuck the remains inside the fitting?
i did same thing but removed centrepiece altogether and replastered small area and painted and now looks fine - less hassle than i thought and was relatively small job - these centrepieces are normally just one piece of a plasterboard material so they can pop off sometimes without have to tear down the ceiling
You'd certainly need to make sure that the live and neutral don't short by keeping them wired to a small wiring block or at least taping them up to isolate them.
Turn off power. Check that power IS turned off. Unscrew fitting top. Unscrew connections to flex hanging down. Re tighten connections to for flex to hold cable in place. Rescrew top on fitting.
You'd certainly need to make sure that the live and neutral don't short by keeping them wired to a small wiring block or at least taping them up to isolate them.