I'm gonna break the mould. While I appreciate regular announcements when a train has been stopped for a while, it does annoy me on the tube when the T/Op decides to immediately get on the PA as soon as the train stops in a tunnel. Trains do stop from time to time in-between stations, whether they're in a tube tunnel or on the ECML. Anyone who uses a train knows this.
So an immediate announcement is not required. In the specific case of the tube, if the train's held at a red signal and it doesn't clear within 30 seconds, then sure, make an announcement saying you're going to find out what's going on (if you haven't already been told), then make another announcement within a minute even if you haven't heard anything back. Making an announcement as soon as the wheels have stopped moving is just too much, imo.
Two minutes on the mainline seems appropriate, and SWT usually do this as well as regular updates.