Move your mortar when you hear the BOFORs start its barrage.
Honestly I can't comment on Counter Battery, because I've never actually had someone use it against me, have never used it, and my AT partner that is really heavy into the Emplacement Doctrine insists that it doesn't even work. He says he's never noticed it do anything, though he also isn't the most astute of players.
I assume that Counter Battery has some foreshadowing of its bombardment? Smoke, or artillery noises? That it costs munitions, at least? I don't know.
I normally beat emplacement brits within ten minutes so I really can't say.
Counter battery is pretty key to this whole discussion about Brit emplacements. At least in 2v2. I've played like 20 2v2s with that setup and it's frightening what it does to enemy mortars. I have a now sadly broken replay of my Brit ally's counter battery slaughtering like 4 mortars and 3 ISGS on Crossing. It's all we've been doing since that commander was released and it's glorious.
Counter battery is free and isn't very accurate but has a good rate of fire. It also covers the entire map on most maps. You just turn it on and your base guns automatically wreck enemy mortars. You can leave it in the whole game except that you can't build tier 3 and tier 2 units while it's on (if both guns are set to counter battery). But it's very easy to have at least one going the whole game.
Mind you this is not at high levels of play. So maybe for people who are better at the game it's not an issue.