Did the announcements used to be any more frequent than now? I know some people have said that the ones on trains used to be every 10 minutes or so, but my experience travelling from Swindon to Bristol with GWR from the past year has been that the See It, Say It, Sorted announcement only plays on approach to/from Bristol Temple Meads if the train terminates/starts there (if it's travelling to Weston Super-Mare then it doesn't seem to play). At other stations the train drivers will often, if they are doing a live announcement, say something along the lines of "if you see anything suspicious then speak to one of our staff, or alternatively you can call the British Transport Police on 101 or text them on 61016" but without any mention of the See It, Say It, Sorted slogan (which I believe some of the staff find a little tedious). The frequency policy may vary by train operator (GWR are expensive but I will give them credit for keeping unneccessary announcements to a minimum and the announcement volume at what I feel is the right level).
I think the announcements have recently been refreshed in recent days, although I don't think many trains have adopted the new ones yet (the original/still standard one goes "If you see something that doesn't look right, speak to staff or text the British Transport Police on 61016. We'll sort it. See It, Say It, Sorted.", with the voice varying on station/train operator but the script remaining identical). I believe the new ones make more specific mention of things like unattended baggage or a person trying to avoid police officers or staff. As far as I know there have been announcements or notices at British train stations regarding unattended baggage since the 1970s or 1980s (although I think they increased from 2005), and the See It, Say It, Sorted ones largely replaced these.