Hmmm, just looked at my FAC, and it just says ".243", no mention of case shape/size.
However, I've got .22 rimfire too, but I don't think I'd get away with a .22WMR on that, even though it's the same calibre!
Of course, it's different, as the .22WMR is considerably more powerful than the .22LR, but it does highlight some of the inconsistencies of the firearms law.
Probably best to tell them anyway, as they are fairly close in performance, so I can't see them being able to complain about it.